This article has advice about identifying and replacing capacitors.
http://www.antiqueradio.org/recap.htm
I recommend replacing all of the electrolytic capacitors in the power supply. They may seem to be OK, or temporarily "re-form," but I have not found them to be safe & reliable to use over the long haul.
See Matt's thread "Only a Matter of Time" from yesterday. An original electrolytic worked for over a year, and then POOF with no warning.
After you have replaced the power supply electrolytics, you shouldn't need a variac except to bring it up slowly one more time while watching for other fireworks. If you don't see any sparks, smoke, or BZZZT at that stage, you can put away the variac.
I don't know offhand whether your TV has a hot chassis ("AC/DC" type power supply). If it has a big heavy transformer connected between the power plug and the power supply electrolytics, then the answer is No.
An isolation transformer can help protect you against shocks from ground, but it can't prevent all shocks. If you touch one hand to a high voltage source on your TV and another hand to a low potential on that chassis, you'll get shocked because you just created a direct path for the voltage through your body. You'll get this shock whether or not you use an isolation transformer.
Use common sense and avoid touching metal things on the chassis with bare hands when it's powered up (or in the case of a hot chassis, simply plugged into the wall). A good oldtimer's practice is to put one hand in your pocket whenever making voltage measurements or other tests on a live chassis.
It's a common beginner's mistake to wire an electrolytic backwards. Pay close attention to the positive (+) and negative (-) connections.
Phil Nelson