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

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.