Speakers are the first piece of the puzzle

Everything prior to speakers have been R&D'd to the point where they can all sound good which makes it more of a matter of taste. Speakers, being the largest generators of distortion, require you to like their sound signature, or house sound, as it's known. 

A well regarded speaker builder told me that the source and speakers are most important, with the nod going to the speakers. Amps were his least concern as long as they were fast. 

All the best,
Nonoise

Jim, I have found after many years of attempting to get a system I could live with in my retirement, I had to make some changes. Much of this mindset was an undying curiosity regarding tube amplification. To find out, a speaker change was necessary. I sold my beautiful Dynaudio Contour 5.4's, and since buying anything new was out of the question, I opted to purchase, on Ebay UK, a pair of vintage Tannoy HPD 315 drivers w/crossovers. (This was a return to Tannoys, I had my first pair of 12" Monitor Golds in 1971, and due to a major lifestyle change, away went the Tannoys in 1988). 

I had a pair of 150 liter bass-reflex enclosures made, that was two layers of MDF laminated, for a net of 1 7/8', with a weight of 192 lbs. each. To my surprise, they have worked out well with either my SET 300B amp. or my kit-built Class D Audio (running two modules bridged for 500 Wpc) The Tannoys sound beautiful on either one. By this time I had already established a pretty good base of source components, making upgrades as necessary due to attrition (failure from age related issues).

So for me, it's been speakers first, to match speakers/amplifier, and then to upgrade source components as the need arises, until I've arrived at the destination that most pleases me. I have no desire to make any changes now, aside from those necessary from equipment failure.

It's an extremely comfortable place to be, listening causes absolutely no angst, just day after day of enjoyment. I hope everyone can reach this lofty goal.

Best regards,
Dan. . 

Speakers alter the sound more than any other component, maybe, unless we’re including analog sources. This should not be surprising, because the speakers must convert the electrical signals to sound waves through mechanical means. Thus, they distort the sound far more than any DAC, amplifier or CD transport.

Whether it’s prudent to buy a particular part of the chain before the others is endlessly debatable.

The OP has it right with the thread title.  The speakers' sensitivity spec and overall performance needs will inform your amplification.  If you're in the ultra high efficiency mode then you can be looking at SETs that have those few, but glorious watts necessary for your speakers.

In my case, with low efficiency speakers, I knew that a higher power SS or perhaps prohibitively expensive tube beasty was going to be in house.

After that it's an allocation of available $ as to the sources, line stage (if needed), cables power conditioning, footers, yada yada yada.  For me it's the yada stuff that's fun.  Eaking out that last bit of musicality by attention to the minute details of the system and room is where the fun is for me. (With the obvious exception of opening the box of new gear for the first time).  Hey...who out there doesn't love that new car smell?

Interesting topic as always. What came first, the chicken or the egg? Let me ask, when one becomes dissatisfied with the sound of their system, what do they change out first? Cables, amp, source, footers (giggle)? I'll bet speakers. Ultimately, that is where the sound (music) eminates from. It's the obvious choice. In many years of this wonderful and sometimes baffling hobby I have found all the links in the chain have an affect on the sound. Personally, I find the speakers have the final say. I've never had a source or amp (or cables) that I couldn't live with. I have had speakers that just didn't cut it (to my ears). Enjoy the ride...