Yeah... So it basically has to work first.
This means power supply caps. Bad filter caps can cause buzzes, hums, pops, small house fires, neighborhood firestorms, etc.
Those are C20, C21, and C22 on your schematic.
Once you are past that, and you don't get any unwanted sound, you get into the quality of the desired sound. That means coupling caps.
The main power tube coupling caps are C12,C13,C14,and C15 on your schematic. These will not only affect sound, but if they are old and (electrically) leaky, they will make it eat power tubes.
C1,C2,C3,and C4 are also coupling caps, and would also affect sound quality based both on their quality and condition.
All caps are not created equal. There are lots of ways to make a capacitor, even for a single given capacitance and voltage rating. Lot's of people have preferences on what types of caps sound the best -- which you can leave in, and which absolutely need to be replaced.
I'm not that particular, but I've found that ones with mold growing out of them should generally be replaced. (Partially not joking -- that is from actual experience.)
This isn't to say that other ones are not important. I'm just mentioning the ones that get the most discussion around here.