what is more important ?

The recipe for best results first shot:

1) Speakers first (taking room into consideration when choosing).
2) Then carefully match the amp that is capable of driving the speakers well.
3) Then match pre-amp to amp carefully as well, if separate.
4) Then top it off with good quality source gear of your choosing. If phono, make sure phono matches to phono stage of amp/pre-amp carefully as well.
5) Tweaks that might help: a) power conditioning, b} speaker placement, c) physical separation/isolation of components from each other (avoid stacking on on another), d) wires (need to be good quality, not expensive, Mogami is a very safe fallback for modest cost), e) also isolate speakers from suspended floors as needed to avoid interactions that muddy the bass and obscure the mid-range

You can start with an amp if you want but that will mean some speakers that might work best otherwise may not be driven well to the max.

What is more important?
I thought Conan had cleared all of this up for us....

The Barbarian?

“to crush your enemies
and hear the lamentation of the women”

Many good points made here. I tend to side with the approach of addressing the weakest link first. Yes, this can lead to a sort of component leap-frog, but eventually you'll end up with a well-balanced system. So don't worry about which component to upgrade first, only worry about synergy issues. If you like making improvements in small increments, with small budget increases, it's best to buy pre-owned.

Speakers then room for me.