Do you belong more to souce first or to speakers first school of thought ?

Generally speakers first, then match rest of components.

Speakers interact with the room, which should be a significant consideration..

OK< I'll bite. Speakers first...but it all matters.

fuses first, then cables...eventually the rest of the system will fall into place. room last.

It is not a matter of debate. The room dictates speakers to some degree and the interface between the two makes up 99% of the sound quality the system is capable of. Next is the amp which has to be matched to the loudspeakers. Everything else is trivial. 

@hilde45 I hope that is tongue in cheek. 

I have one non-negotiable.  SET.  So amp first, then speakers to match.  The source is fungible.

Speakers first then an amp to match.

Speaker synergy with amp is the 1st step in creating a HEA audio system. Preamp over source. I know this might upset vintage or budget conscious buyers but when you skimp on electronics, speakers and source components can not reach full potential.

No one remembers Ivor Tiefenbrun, founder of Linn, "Garbage in, garbage out"?  You can't improve what you don't get/can't get rid of any added distortions from what comes off the record, cd etc.  I've found that as I've upgraded my source, I get more of the artist's intentions, lyrics, instrumental lines, etc.  Of course electronics, cables, speakers, room matter, but you have to start with a high quality source.

The speakers are what I'm actually hearing, so I'd possibly be speakers first, but if the source of what the speakers are playing is faulty. "Garbage In, Garbage Out", or 'GIGO' for short, btw, is an old, old expression - used it with IT along with other systems that take something in and spit something else out, for many many decades. Nobody at Linn invented it. 

If you are talking about creating a system and not planning on gradual, incremental improvements, the answer might be different than someone establishing a strategy to improve the system.  Linestages, followed by digital source components, are MUCH more consistent in their sound than speakers and power amps.  The difference between extremely good versions of these components and more price competitive models is relatively small as compared to differences in amps and speakers.  So, it might make sense to invest a bit heavily in those components with an expectation that they will be good in any system and will be long-term keepers.  This would be a strategy for someone planning to make incremental improvements, whereas someone buying a system that will not be changing much would probably be better off spending more on the amp and speakers.

Speakers and amps and the room housing the speakers should be considered somewhat together.  There are very big differences in the sound of speakers, and they may have extremely different demands as to room placement and compatibility.  Because of such variability in sound, one will tend to make mistakes on choices early on before becoming more certain of one's own preferences and what might work in one's setting.  That might argue for not spending so much on speakers early on in the process.  The amp should at least roughly match they type of speaker it will be asked to drive in terms of power output and compatibility with the impedance curve of the speaker.  For example, a tube amp with high output impedance might not match well with a speaker with a low impedance that also has other related demands.

I personally find certain types of amplifiers to be significantly better sounding than other types (I like low-powered tube amps), so any speaker candidates will have to be compatible with that category of amps.  It is MUCH more important to prioritize the right choice of amp than it is to prioritize choice of sources or the linestage-- good choices there will almost always be good with whatever choice is made for amp and speaker.  

To me, the source is somewhat discrete relative to the rest of the system. A crappy source will sound crappy with whatever follows. However, the speaker/amplifier relationship is much more symbiotic, as several here have said. I believe somebody mentioned matching the speaker and the room but I haven’t seen anyone yet mention the relationship between the type of music listened to and the speaker. Sure a good speaker should sound good with most music but not every speaker can handle the power to fill a large room to believable levels with hard rock music, as one example. Also, speakers can alter tone as not every speaker projects a flat frequency response so some offer a presentation that seems to add a bit of warmth while others can be perceived as providing greater detail. In addition, loud is not enough for some types of music or for some listeners where there needs to be a feeling of weight and power behind the sound, as it is in real life. Conversely, not every speaker sounds good, or realistic, at low volumes. Having subs, or not, can also make a big difference.

All that said, I would start by finding the right speakers for my room, music, and listening preferences, then match an amplifier that can drive them convincingly, and finally work on improving source components. I view the preamp as sort of between the amplification/speaker side of things and the source, as in my experience the right preamp for a system can make it sound wonderful while the wrong preamp can be similar to ruining your favorite dish by adding the wrong spices or flavorings.

Speakers + room for me. I have a loft that is medium size but it opens to a stairwell on the left side. That means the left speaker is separated by the stairwell with a half wall while the right is adjacent to a typical 9' high wall. Not all speakers like this configuration but it's what I have. Given that my open baffle speakers really shine in this room with only minimal corner treatment. 

In summary: 1) sort out the room for the best listening position, 2) choose speakers that work well in the room, 3) adjust any treatment to account for room issues, 4) build the front-end that makes the whole system work. 

Personally I really don’t belong to either / any, because it all matters. The generality of the speakers matter most is a good rule of thumb for the folks fairly new to pursuit of the high end… but it holds best when one has appropriate portioned investments in system components with traditional speaker technology. But can be wrong with specialty speaker technology (ie, planar) unique individual components of systems.

For many years I believed in first getting the source right\.  In the course of that, I think my source/speakers ratio became way source heavy.

the hierarchy of priorities is not the same at all levels of overall system performance.

for low and medium level system performance (1) speakers dominate the performance equation, followed closely by (2) the speaker/room/acoustics relationship, then (3) the speaker/amp relationship.

use to be that sources really varied in performance. these days finding a decent/cheap quality digital source is simple. and with streaming even media is a non issue. and decent analog is also easy to find.

so the days of the source limiting most system’s performance are in the past.

towards the top end of system performance it’s the room and sources + media that are more dominant than speakers. lots of good speakers. but great rooms and top level sources are still significant past a certain level of speaker performance.

the tip top digital or best tapes and original pressings + a really super sounding room takes the prize.

Amp first approach is less common but I can understand that. To a degree I would follow it too because I want to use tube amplification, though not necessarily SET, and some speakers just won't sing with tubes.

I think, I almost fully agree with what Mike said, generally speaking.

! agree with @hilde45 🤣

Mike

Speakers first camp here. That way you can make sure your room layout is good for the speakers and the amp matches the load requirement for your speakers

Speakers because they are the final frontier between your ears and the music!

The room can be taken out of the equation because you the listener can sit in the nearfield - 2 meters/6 feet away. I do that with my current system due to space constraints.

Yet speakers are passive components compared to the source and amplification.

This is a no brainer.........."SPEAKERS" always first!!!

I suggest a wild assumption that everyone here does have brains. Any objection ?

Having owned a Audiostore and experimentation ,I feel the quality of the source  is 

most important , speakers a close 2nd why ?  For the quality of the source is what makes the audio signal ,good or bad , once it goes to the next component it is just that ,it cannot be improved upon. Even if it was the finest speaker ever made.

if the instruments tone ,and Soundstage is not there then the Loudspeaker  cannot 

reproduce what it does not have . The Loudspeaker is though right behind the source to finalize the creation of the original signal, From Start to Finish.

I have an impression that the more experience audiophile acquires the more he appreciates the importance of the source, even given the same recording quality of the material. I used to be more speakers first guy but no longer, now I am more source first guy.

And the higher end your system is the more important source is, as Mike said.

Chicken, or the egg…

Source. Sometimes speakers. Depends on what I want to listen to. 
 

Switch gear around a fair bit. Sometimes I want to listen to a SE tube amp - that will dictate speakers. Sometimes I want to listen to Class A SS. Then I have options w speakers. Sometimes, I want to listen to a high sensitivity speaker. Again, then I have options w amps. Decision gets made for me if I put low sensitivity speakers in or a low powered amp. 
 

But as said above, it all matters. 
 

If I have to choose, then source. Garbage in, garbage out. 

Good source will sound better on mediocre speakers than mediocre source will sound on good speakers. And FWIW, there are some pretty damn good inexpensive speakers out there. Let's just call it at $1000 per pair tops and that you've got an average size room. I'll start with Monitor Audio, Polk, even Revel have very respectable offerings.

I’ll go with speakers,  but as someone else mentioned previously, I would put a lot of consideration into the room and what type of speakers would perform best in that room.

I’ve followed the path of source first. Better pressings/recordings..

And even with my first turntable, the first upgrade was the cartridge.

Then often the speakers, then amplifiers, room treatments and then back to turntable again.

But speakers are the soul of a system and in this sense they are always the most important element.

If the source is terrible then nothing matters and the same is true for the speakers. That said I think the variance in speaker quality is more impactful than the source. I focus on speakers first. I have Sopra 3 speakers and they contribute the highest single cost of my 125k system. So as you can see there are many other contributions to the total. I have vinyl, CDs and streaming so this is a multiplier. Also cables make up about 22k of the system. It all matters. Then there is the influence of the room. If it is a bad room a lot of the effort will never pay off. 

If you measure distortion in a contemporary music reproduction system on a per component basis, speakers contribute orders of magnitude greater distortion than any other component. At least in solid state and ultralinear tube systems. We are talking single digit distortion percentage figures versus 0.000025%. So it’s not even a question for me.

1. choose the speakers

2. place the speakers (you can do this with math and geometry, there is a right spot)

3. fix the room

4. fix the speakers

5. choose a signal standard (I favor +4 dBU but if you like -10 dBV you do you)

6. choose your components

7. fix your gain staging (if you have components that will let you do that)

8. now you are ready to hear various source components on a level playing field

The listeners chasing euphonic distortion with low power amps and very sensitive speakers 105 dB/W or more!) are playing in an entirely different sport and may have different rules entirely.

Budget, then wife, then room, then speakers.

It all matters.  Having said that I don’t think that the emphasis on the source should be what it was 50 years ago because the quality of the sources has improved so much.  Midfi turntables and digital sources sound pretty good these days, as a rule.  I’d rather play a $1000 streamer or turntable through $10K speakers than the reverse 

In regard to this subject,  back in the mid 1980's  I was visiting a Linn Naim dealer who had some articles written regarding audio.  One was called "The Hifi Hierarchy" written by Linn Audio founder Ivor Tiefenbrun.  Here,  Ivor described how the front end of the audio system was the most important part of the system.  More so than its amplification or speakers.  Ivor's rationale was simple enough for this belief. Specifically, that it is impossible for amplification or speakers to correct the deficiencies produced by a source component. As such, Linn Naim dealers would encourage those interested in purchasing a new audio system to focus most of their expenditure on a Linn LP 12 turntable, and then build the rest of their system around the LP 12.    Dealers would often sell LP 12 turntables with Naim Naits and Linn Kan speakers, and then allow their customers to trade in the equipment for full value within one year of the original purchase in order to upgrade to a better Naim amplifier and Linn speakers.  This program worked quite  well during the 1980's and was quite lucrative for both Linn and Naim as well as their exclusive dealer network. Eventually both companies  went their separate ways, but back in the day, they had one of the most successful partnerships in the audio business.  

It's intuitively clear that "high end" speakers can't deliver their promise with "low-fi" sources/amplification, but I have never had that personal experience. Reason: full-range floorstanders, unported yet with good bass extension, were beyond my budget. So, while I could swing $2k amp and $2k preamp, $2k was also my limit for speakers. Only after substantially upgrading the speakers did the system come alive. Same electronics, same room, same configuration. Ever since, I have held to this maxim: never spend more than 60% on any component, upstream or down, than you paid for the speakers. (Well, I already knew the maxim, but couldn't afford to honor it). So, for those who endorse OP's binary framing of the question, I am on the speaker side. 

Interesting responses here, and probably no one correct answer for all situations. Today’s digital front end equipment has been changing and improving rapidly compared to speaker and amplifier technology. Just look at the number of new digital front-end products that manufacturers have released in the past few years and claim to improve on their predecessors.  Also, it is much easier to try different front end components than to cycle 100-pound (or more) speakers and amplifiers in and out of a listening room. However, as many here have said, getting both the front end and the amplification/speaker right is important, as is having a system that is complimentary to the other components, the room, and the listener’s music and sonic preferences. This is really a chicken and egg type question where it is one or the other until the listener achieves a balance that results in their satisfaction.

Budget first

then build

Usually agree speakers are deciding factor on a lot. On my current system, I got KLH Model 5;s. They sounded great, plus also looked great with my vintage system. Good size, good sound, good looks, good price. Played with them for about a year, then got Klipsch Forte's. This changed everything. My systems was much brighter, bass much deeper. However, it sounded like crap! Going from 89db to 99db sensitivity showed me everything that was wrong.The Klipsch showed me that I had a ton of noise in my system, my preamp has a slight hiss on the right channel.

What did I do? Got all new cables, pulled all components, cleaned everything, put back with all signal on the right, all power on the left, added a power conditioner,  My amp is huge, also had to cut out the back of my cabinet to fit it. 

In my quest, the speaker first cost me a lot of unintended money, but now sounds wonderful. 

+1 @jpwarren58 

This source/speakers match is a very interesting and complicated subject by itself.

Matching doesn't mean efforts to literally directly compensate, it usually requires a lot of thought and experimentation. It is easy to completely screw up the sound, to throw it in disarray. But I would guess that, generally speaking, your choice of table/arm/cartridge/phono stage should not be too different than your choice of speakers. The idea is to make the speakers sound their best, not to make the speakers sound the way they don't really want to sound.

So, in the end the source might be more important but you choose speakers first and upgrade them last. At least, that's how I see it.

I bought my modest speakers 25 years ago but the sound that I have now is light years away from what it was. Everything else was upgraded.

Good source will sound better on mediocre speakers than mediocre source will sound on good speakers. 

I think that there may be something to this.  

I would have defined "source" as ALL the electronics in front of the speakers, but I am thinking for the purposes of this discussion, that "source" refers to the first front end component in the system? 

Good source will sound better on mediocre speakers than mediocre source 

I consider my CD player and TT mediocre and they sound great with good speakers and bad with OK speakers. So I guess it depends on the definition of mediocre. To translate this to numbers:

$200 CD player - $1000 speaker or 

$800 CD player - $400 speaker?

(as speakers budget shouldn't be 1:1)

Note, I didn't forget one "0" from each number - that's what I meant 😊