A Variac is a great thing. It's been always in my wish list.... I use the light bulb trick which is nice, so I haven't bought a variac yet... Some day.

Try the light bulb "current limiting" thing. It's a very useful dirty cheap gadget.
I work in audio gear also, as a hobbyist. Guitar tube amps and any kind of outboard studio gear. If dealing with amps, follow Dave's recommendations. Almost all the gear and tools he mentions is worthy in any audio gear related lab. But also, make some dummy loads from good reliable power resistors (or a single switchable/rewireable one), grab a good old analog scope for cheap and save a few bucks. You won't need latest sophisticated "Nasa level" scope for this.
About the signal generator you won't need a sophisticated one. Driving sine waves is more than enough for this task. You can also check the Hoffman amps site for that kind of DIY "sthetoscope amp" for specific testing driving the circuit with actual guitar signal instead of sine waves to actually hear what's going on in any part of the amp. Sine waves are great for initial tests, diagnosis and repairs, but they tell only a little about sound or complex signals like guitars signals are, as well as how good or bad a particular overdrive/distortion/non-linearity sound to our ears. So for setup and tweaks this is a great tool that can be made of a cheapo second hand amp. Those weird amps that nobody seems to want and sell for peanuts.
This is a non sense tool for most audio gear, but guitar amps should play "beautifully crap". That's why we love 'em.