Relative component value to overall SQ.

@n80 ,

One consideration not yet mentioned is if you are buying new, used or doing any DIY. Where I'm going here is that if you are buying used, some types of components depreciate more, allowing you to get a good balance for your budget by spending less on those items. I know you excluded sources from your premise, but I think you can't wholly set that topic aside because digital gear depreciates more than anything else.

While speakers, amps, preamps etc. typically sell used for ~half MSRP(yeah it can vary by brand, age, etc.), digital used gear more than a year or two old can often sell for 25%-33% of MSRP. So I would suggest used digital a smarter investment if you are a beginner on a budget; it may not have all the latest features (often formats that don't ultimately catch on - e.g. HDCD, MQA, etc.). Cables have really high margins and older ones a few iterations older, often way better value. Used pro cables like Mogami or Canare sound really good and can be had for very little cost. 

IMHO, room treatment and speakers will have the biggest variation in sound and choosing speakers that suit your personal preferences/priorities and room is the most important decision. Speakers cost money, so invest some thought & elbow grease to improve your room at low cost. Since even without soldering & electronics skills, most of us can handle a staple gun, scissors and a saw, DIY room treatments can significantly improve your overall sound at a modest cost. Don't make the mistake that many make and ignore the room because they prioritize all the budget to other items. You may also be able to utilize furnishings you already own towards this goal. Natural fibre rugs, thick curtains and bookcases full of books can be wisely deployed towards in this effort. Covering windows, moving glass-frame out of harms way and added upholstery all can help too.  

In terms of choosing components, pick an easy to drive speaker if you find one that you like. That will allow you to spend far less on amplification. Choose the best quality (not most powerful) integrated amp that mates well with that speaker. By going integrated you will need fewer interconnects and power cables. Assuming you are spending less than $5k on the system, solid state will probably be your best bet strictly because tube amps usually cost fare more $/watt. Until you get up there in total budget, good tube stuff isn't really an option unless you over-allocate on the amplification. 
So bottom line, used speakers 50%, used integrated amp 25%, used cables(speaker, 2pr interconnect, 2 power) $400, DIY panels $200-400, the remainder on sources. Cheers,
Spencer 

@bdp24 Great post! 
That's why I suggested used. Think of it as home audition for as long as you want at marginal cost. If you goof on a match or your priorities change, flip it with little risk. If one assumes that they may not hit perfection on the first try and are willing to enjoy the journey, it can be a fun, long and winding road(that leads me to your door - just like a Fedex delivery!). Cheers,
Spencer

@elizabeth On the role of room acoustics as related to this topic, I would encourage @N80 and others that for a beginner it doesn't have to be complex and in some ways, you don't even "need to know what to listen for".
Most beginners choose dynamic (cone driver) speakers and they almost all emit sound at wide angles that result in sound reflecting off the side walls that hurt sound quality. Doesn't matter if we are talking floorstanders or monitors on stands, they all do it, mainly from tweeters & midrange drivers. Absorptive panels at the first & second reflection points, will almost certainly reduce echo and improve clarity of vocals and higher pitch instruments. Inexpensive options like these
https://mioculture.com/shop/wall-ceiling-tiles/acoustic-weave-paperforms-white
or DIY homemade alternatives made of Owen's Corning fiberglass from the local hardware store are worthy of consideration.
Absorption of floor reflections with a natural Fibre rug between seat & speakers almost always help, especially when dealing with hard flooring of tile or wood, but also with synthetic carpet.
Glass windows are super reflective and natural fibre heavy upholstered curtains will tame them every time.
By playing a test tone CD of varying frequencies one can easily identify bass interactions with the room. Many rooms inherently have certain frequencies that play too loud(peaks) and others not loud enough (dips). The extent of those anomalies will be an indication of if bass traps in the corners behind the speakers would be a help or not. Fixing bass issues is sometimes pretty tricky, but I am confident that you will get the point. 
I find it frustrating when folks spend big bucks on gear, ignore the room issues and later lose enthusiasm for the hobby, because they aren't drawn to the music playing on their system. Rooms need to be conquered and it's not that hard nor expensive to do so.
While a DSP approach might be an alternative, I  have always been leary of adding more cables and boxes, as the chance of noise and grounding problems increases. Perhaps newer DSP solutions exist that surpass what I have heard. Cheers,
Spencer