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

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.