I have very limited experience with test equipment so I can't really give any specific recommendations. I'm just a student at the moment- a more senior individual can provide better advice. Here's a breakdown of what I have:
*Extech EX330 multimeter
-Has extra features like a capacitance meter, frequency counter, temperature sensor, and a diode checker function.
*HP 3312A function generator
-Basic sine, triangle, and square waves with symmetry adjustments and AM/FM modulation as well as sweep capabilities. It only goes up to about 13MHz so it can't be used for broadcast FM radio.
*Rigol DS1052E oscilloscope
-50MHz scope, easily unlocked to the 100MHz model. Brand name parts throughout (even the buzzer is TDK!) but the Analog Devices ADCs are overclocked from 40MHz to 100MHz so that they can get 1GSa/sec. I don't have this yet but it should arrive very soon.
*Precision 612 tube tester
-Tests for shorts and shows how well electrons can flow from the filament to everything else. Transconductance models do a more "real-world" test but cost much more. I also don't have this unit yet but it's in the mail.
*Variac model SC-3M
-Allows me to vary the AC line voltage. I use it to bring up items under test to verify that the voltages are proportionally correct before applying full wall voltage. I also use it to slowly bring up my MAC 1500 to extend the life of the tubes as I had issues with the standard route. Usually you can install a GE CL-90 NTC thermristor in series with the AC line to "soften" the turn-on jolt. It ran so hot in the cramped power section of my MAC 1500 that it melted the solder... very bad. Use only if you have breathing room for it.
*375VA isolation transformer
-Makes operating on live equipment a little safer. See this post on Hack a Day for more info. Operating on live equipment is never 100% safe though so be sure that you're taking proper precautions. I always wear shoes, remove my watch and sit on one of my hands when I'm probing a live circuit.
*Hakko 936 soldering station
-High quality pencil iron with a temperature control. Much more of a pleasure to use than my old Radio Shack model. Well worth the $.
*Weller 8200 N 140W soldering gun
-The Hakko is really only suitable for PCB work. Everything else, like the radio I'm restoring, needs a more powerful tool. My Weller heats up in seconds and can solder to even the largest of metal surfaces if enough flux is used.
*Radio shack desoldering iron
-Great for removing huge blobs of solder, unreliable for removing enough to remove a component.
*Techspray #3 solder wick
-Sucks up solder very well. Works much better than the stuff you can get at Radio Shack.
*Fan
-Solder fumes aren't the best for your health. I always work near an open window with a fan blowing outside.
I hope this a) is helpful and b) doesn't scare you off! I acquired all of the above over a 4 year period. I was able to restore the MAC 1500 with only the multimeter, variac, soldering gun, and desoldering iron. Since I didn't have an isolation transformer I checked voltages by attaching an alligator clip to the point of interest while off and then powering it back on.
Edit: a word of advice while we're here. If you ever see a large metal FP style capacitor and you're not 100% sure that it's perfectly operational (current leakage especially) REPLACE IT. Don't power the unit up. They can explode like a hand grenade and send shrapnel flying everywhere. I myself replaced all three such capacitors on my MAC 1500 with brand new (not NOS) units to avoid that possibility.
Edited by MCC - 6/26/11 at 8:59pm