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

Chicken, or the egg…

Source. Sometimes speakers. Depends on what I want to listen to. 
 

Switch gear around a fair bit. Sometimes I want to listen to a SE tube amp - that will dictate speakers. Sometimes I want to listen to Class A SS. Then I have options w speakers. Sometimes, I want to listen to a high sensitivity speaker. Again, then I have options w amps. Decision gets made for me if I put low sensitivity speakers in or a low powered amp. 
 

But as said above, it all matters. 
 

If I have to choose, then source. Garbage in, garbage out. 

Good source will sound better on mediocre speakers than mediocre source will sound on good speakers. And FWIW, there are some pretty damn good inexpensive speakers out there. Let's just call it at $1000 per pair tops and that you've got an average size room. I'll start with Monitor Audio, Polk, even Revel have very respectable offerings.

I’ll go with speakers,  but as someone else mentioned previously, I would put a lot of consideration into the room and what type of speakers would perform best in that room.

I’ve followed the path of source first. Better pressings/recordings..

And even with my first turntable, the first upgrade was the cartridge.

Then often the speakers, then amplifiers, room treatments and then back to turntable again.

But speakers are the soul of a system and in this sense they are always the most important element.