Amp first approach to building a system, anyone ?

I would first select your speakers as that choice can determine your choice of amplifiers.  Very efficient speakers don't require the high power and speaker impedance has some to do with amp selection too.  Efficient speakers with relatively higher input impedances can be driven easily with flea-watt amplifiers such as 300-B tube types and First-Watt low wattage amps for terrific sound.  When I moved from 98db/12.9-ohm speakers to 88db/4-ohm speakers, I had to seriously change amplifiers. In any event, you should choose an amplifier that can provide headroom of ~ 10db above your higher listening levels to allow for high transients (headroom) reducing the risk of clipping.  

My long audio journey over the past 50 years started piecemeal to take advantage of roommates equipment also, so actually first purchase was a TT. Then gradually building system all my own. Then many many individual piece upgrade or experiment.

Cant say I am amp first, though after rolling through several, I have repurchased one of my previous that I end up preferring.

like @pindac  I would say I am polygamous. I have both SS and tube amps, 2 phono preamps, and 2 pairs of main speakers (of different designs).

I find I can satisfy my need for variety while also have well-matched components.

(Also have a herd of vintage components)

I like single ended triode amps, but I do not want to deal with speaker cabinets, which are engineered as the famous flying wing aircraft designer put it, "invent rubber gloves to write with leaky fountainpens." That limits me to planar magnetic speakers. I use Magnepans which sound better than a pair of $50,000 + speakers that have cabinets. But they need mor than the likes of 300B SET's can produce. 

I took 46 bulb SET's and used Lundahl interstage transformers to go from 5k to 600 ohms that I coupled to the grids of 833A triodes run at 1000 plate Volts and Hammond output transformers to Magnepan 0.7's and bass panels. The 833A needs the purest DC for the 10 Volt 10 Ampere directly heated cathodes. You can do this modification for about $1500 or less and it will have better parts than a WAVAC 833A pair of monoblocks costing $480,000 or more as inflation takes over.

Common acoustic sense is this ideal order:

 1---Room geometry,topology acoustic content and parameters first....

2---Speakers  must be adapted to the room and chosen location and picked accordingly ...( you dont put 5 inches subwoofer  in a Trump ballroom) 

3---Amplifier exist to serve the chosen speakers mainly then third...

4---Dac source or turntable must serve the amplifier and the system/ears then  last ...

You can buy the dac first for sure, i spoke about ideal order of electrical and acoustical synergy ...

I suppose if someone is in love with his speakers they were chosen for a specific room and needs, the same is true for a pair of chosen amplifier serving a set of speakers... Changing one will imply a choice determined by the one we kept ...

What cannot change is acoustics, the link between the room and the system to your head/ears, is the only link that guide us all ...

Then anything else matter less ...Even our "taste"  for a brand name speakers or amplifier is secondary because we cannot know the sound qualities of a system/room before we experimented with it ...

The ultimate rule i discovered in audio hobby is this :

Any picked  system/room sound completely different on a quality scale before and after the implementation of the  tetrad of factors entering into the optimization process (mechanical,electrical,acoustical&DSP ) 

Then this rule has nothing to do with "taste"  but everything to do with basic knowledge... Anything else is the result of marketing conditioning ...

 Once this is said we all have our "taste" born from our own audio history of purchase... I like my Sansui amplifier and i miss my Tannoy speakers...

@inscrutable Great to be sharing space with an individual who has a passion for using audio equipment in more than one permutation for a system.

I also like the reference to the two different technologies belonging to owned Speakers.

I have been ESL and Back Loaded Horns in the early days and then Horns were swapped out by various Cabinet Speakers, either Two Way on Stands or Floor Standing Three Way. This evolved into Co-Axial High Efficiency and then the Wonderful Cabinet Speakers I am very recently using that has put my ESL Speakers into storage.

The systems End Sound is the Speakers function, learning how a variety of Speakers function is able to shape and form sound in the listening space is a great experience and worthy of encouragement.

Even musicians swap out their favourite instruments, so why not experience a different shaping of a sound from a signal generated by a audio system, solely for being converted from a Electrical Energy into a Kinetic Energy in the form of a Sound Energy.  

Off Topic but relevant to audio experiences had, I changed many many years past.

The audio system was removed from being seen as a alter and the listening space a sanctum, where I was to reside as a Hermit. What a life changer that was when abandoned.

For want of a better description I became a mingler and travelled far and wide to mingle with other audio minded individuals who were content to mingle.

I became a host and through becoming a host, become a educator and become much better informed and educated from my evolving friendships. Whar a life changer thsat has been since being adopted.

 I think today of this structure formed around audio and the regular offers of being participant somewhere, as a Holistic Audio Experience. Where the audio experience is assessed (if assessed at all) by the enthusiasm of the individual for it, but not their creations for a audio experience. The individual is an audiophile through their passion to experience recorded music replays on purpose produced audio equipment, finding that passion stimulated in any environment where recorded music is to be replayed on a purpose produced system.

The individual is certainly no to be assessed on how they have eked out of a system a so called ultimate Hi Fidelity, leave that one for Mr Hermit, with their only ever hearing one system and no system is more Hi Fidelity than theirs attitude. 

The pain Mr Hermit has to endure within their poor head, with their purporting how right they are and how cool they are.    .