Well, everything changes over time, but old transformers are well valued by many DIYers. I would start with the caps first, because new caps are often much better in terms of tolerance. That being said, it could make your amp sound very different than the old sound you are used to.
I would also suggest looking at any wires and perhaps RCA jacks as well before you venture into anything else.
Take it slow, one step at a time until you are happy with the new sound.
Bob