Heathkit gear is a good place to start learning about audio electronics with one exception: they were kits to start with.
This means that someone likely built it. On the assumption they were also wanting to learn about electronics, there may well be all sorts of little things that can now cause problems in addition to the aging capacitors.
I'd suggest you first go through the entire unit looking for cold solder joints and pinched wires. Look for any wire that turn corners, are tightly bound, may have been over heated. Wiggle all solder joints especially those where wires are attached to boards. Many of the boards were pre-stuffed in bigger Heathkit projects and the user only had to solder them together after assembling the chassis parts.
It is best if you have the original assembly manual, too, as this will have the step-by-step process for you to follow - something alone that will help your understanding. It will also have all the alignment and setup steps.
While you are in there, also look for bulging capacitors. That is, there may be electolytic caps where the small can or tube may have expanded. The tell-tale sign is the plastic shrink-wrapped used for insulating the exterior will appear to have shrunk and parts of the ends of the metal tube will appear to be extended beyond the ends of the insulating wrap. These have to go, of course. I am working on a HK Citation 16 of the same vintage as yours right now that has this problem.
Hope that helps a bit.
Cheers,
David