You don't need a truckload of test equipment for your first TV restoration. It would be nice to have some indication that the CRT is good before you spend a lot of time replacing capacitors, which is usually the most time-consuming restoration step.
If you don't have a tester for the other tubes, you can least test their heaters to see if they're duds. Put the ohmmeter probes on the heater pins. Infinite resistance = dud. Resistance of a few ohms means the tube should at least light up, although it may still have weak emission. You can look up tube data sheets here:http://tubedata.tigahost.com/tubedata/
If your tubes are OK (or semi-OK), then I would start by replacing the electrolytic capacitors. This article has basic info about recapping:http://antiqueradio.org/recap.htm
Powering up with new electrolytics might give you some signs of life.
Next phase would be to replace small capacitors. This article has some info about replacing caps on PC boards, if that's not obvious to you: http://antiqueradio.org/PhilcoF4626MTelevision.htm
If you are lucky, then OK tubes + new caps will give you a TV that works, at least somewhat. Matthew's discussion, referenced earlier, has good specific info about this model.
If it still doesn't work, then you can think about debugging specific problems, and at that stage some of the test equipment may come in handy (assuming the equipment works properly).
This TV doesn't have a zillion components, so if you want to think of it as a practice project, you won't be investing a lot of money in parts.
Phil's Old Radioshttp://antiqueradio.org/index.html