Well, I hate to be the bearer of bad news, but a Fisher is not really something to start on, they are or can be quite complicated and a bit pricier to fix as they used more components for their units, so expect at least $25 in just capacitors, both paper foil, crossovers, and filter capacitors. They are a bit complex so thankfully the tuners at least work, so the work cut out for you is less.
Let's not focus on the turntable for a bit, as turntables, ESPECIALLY Garrards, are an abysmal nightmare to completely clean out and relube. They are better performers but boy are they merciless to newbies.
The first order of business is replacing the power supply capacitors, IE the large silver can capacitors that are near the big transformers. This is what provides your main voltage rails and when these rails get noisy, you have hum. Since the hum varies with the volume control, that indicates that the hum is introduced into the control, which could be a failing or noisy tube, or even a noisy tube socket that needs to be cleaned and reseated. An easy way to confirm this is to tap on the tubes with a soft object and see if any noise comes out of the speaker or if the hum goes away or cuts in and out. This could also be caused by a failing capacitor introducing DC on the tube.
Good luck with your work and if you need any assistance, I am sure TC Chris as well as I would be happy to help. Happy recapping!