How would changing tubes affect amp sound?

Not much is how much.

The audience won't know the difference unless the old ones were dying.

Brands don't matter as they're made in one of three factories.
Ruby's are Chinese, JJs are Eastern Europe, and EH/Sovtek are Russia.

Some resellers have exclusive deals on certain(old) designs from certain factories, but the difference between them is marginal.

The biggest differences come from using the wrong tube for that slot.
Generally it'll cause alot of brightness and a big volume boost(putting a 12ax7 in a 12at7 slot in a Fender) or a big gain reduction and dulling of the tone(reverse).
Only the second applies for you, as you have 2 kinds of tubes in there.

Change the speaker if you want a bigger change in tone. The C30 has a very midrangey speaker in it(which is why I went with the Delta Blues).

A set of tubes costs less and is not as permanent a change on an amp as swapping a speaker, which will void your warrenty if you bought it new. If you swap them out, you also will now have an extra set of tubes as spares, which can come in handy if you play live and run into some problems.

I had a Peavey 5150 combo and it was unbelievable how much difference a matched set of preamp and power tubes improved the sound over the stock tubes. It really opened it up and took out a bunch of hiss that was present at stage volume.

I do not doubt that changing speakers would make a greater difference, as a V30 does sound way different from a Greenback or an open to closed back cab. If the amp is under warrenty and you want to try it with some other speakers, I'd look into getting another cab and using the combo as a head.

A speaker swap takes 10 minutes at most and is invisibly reversible.
Peavey won't care if you take it in for service, as long as that's determinted not to be t he cause of the problems.
The service would be done at a local service center anyway, and by the people you bought it from.
Peavey uses Ruby's now, which are a little hissier under tons of gain*5150* than others, but again, neither of those things will be noticed by the audience.

Why not first try an EQ pedal?

Good point.

I'm amazed. This actually makes sense (I was researching on a ton of sites that sounded like gobledygook and felt pretty dumb). Thanks!

it also depends on the amp circuit itself (how big a difference swapping tubes will make). but everyone more or less OTM. but the problem with an eq pedal is that it wont necessarily get you quite what you want... it'll change the pre-gain tone character, whereas tubes happen pre- and during- gain stages, and speakers happen post-gain and have their own set of distortion characteristics.

swapping tubes in my fender hot rod deluxe improved the tone a TON, and i have no doubt that a speaker change would have improved it just as much again.

The classic 30 has an effects loop.

but it still wont come after the PTs and speaker...

i guess that wont matter so much depending on how hard you drive it...