The big issue with old amps is the caps going dry, leaking, etc. and that’s what the variac should help you with. That is, they'll help you blow a fuse before you do too much damage. When those caps go bad they can take out the rest of the amp with them.
Before using though, open it up and take a look around the biggest caps you find. They’ll look like soda cans with screws. Check them for any sign of corrosion or leakage. If it looks like the Coke or Pepsi has seeped out even a little, or the cans are bulging have it serviced first.
Do the same for any of the smaller caps too. Inspect them for obvious bulges or leaks and at any signs of degradation take them to be serviced first.