Surprisingly many grades of stainless cut very well and give a good edge finish (not so much on a galvo but on a flatbed where you can have gas shielding) 316 (S32) is great, takes a bit of power but quality when you get it right is amazing.
As a rule even the metals that respond well to fibre cutting on a flatbed don't do so well on a galvo as although they may use the same wavelength they are very different animals.
Quality wise, with power being a given, I'd say stainless steel sheet and aluminium both give great results, (Al being one of the worst metals to cut for power requirements though)
Avoid copper, nimonics, stellites, high carbon steels (EN16, 24, (T) etc), bronze is an absolute belter to try and get right (so probably don't go there) Brass....varies a lot
The problem is, power and density.. galvo systems typically have some funky beam modes due to the very long focal lengths (and mirror irregularities) anything under 300 watts is simply the wrong tool to be using to cut metal. On budget I'd probably use my plasma system, about the same cost as a Galvo and 1000x faster.
hope that helps a bit
Rob above posted a couple of great videos that demonstrate the failings of Galvo's