The question as always is input labor, time, and $$ versus usefulness of output result. Maybe if this is your first project, you'll have so much fun doing it that none of the above will matter. Maybe not!
Some of us scrounge old gear and try to convert it into guitar amps. Some folks never do this. Although I scrounge, it's my opinion that such projects almost never turn out as nicely as buying the right chassis and all new parts.
Most tube equipment, with the exception of powered radios (by powered, I mean having a real output section aka 2 qty 6V6 or 6F6 (as you might find in yours) will not make enough B+ using the existing transformer to really make a Champ or a Princeton. I have some nice tube based Winegard video line amps, for example. Cute little things, would be perfect for a little Princeton and the power transformer is exactly the same size. Guess what? The PT makes a grand total 120 volts DC on a good day and you need 350. Because back then, a video signal was 1 volt driving 75 ohms (about .013 watt) and that was all the output section had to swing. And ANYTHING more than that just was wasted heat for the user and extra cost for the mfr. Test equipment is like this too. Many many pieces of test gear can make 250 volts and drive 4-5-6 little tubes talking 25-30 mils = 7.5 watts. Oh wait, we have to light up the tubes.....
It is kind of rare in my experience to adapt from existing gear a thing that 1: works, 2: sounds decent, 3: can be carried around without breaking and 4: is as convenient as a combo (meaning speaker and amp in one box)
I never ever want to discourage anyone from trying these things. But when I add up the parts cost of say a Princeton Reverb and add in the time to build it....it just doesn't make sense. Forget not that maybe you do not want to buy a clean used Princeton Reverb today for say $600. You could buy that amp today for $600 and sell it in ten years for $600 so really....they don't cost anything.