[Electronic M]

Personally I prefer leaded solder for working on tube era equipment. It seems to flow and work better with what's there.

Essential equipment: a good DMM (I'd recommend a fluke) and or VTVM, a B&K 1075/76/77 Analyst, a CRT tester ( so before you buy you can make sure you don't have a 80lb paper weight), a signal tube tester ( because testing by substitution/voltage checks in set/guess work is imprecise and can be maddening), test pattern generator or DVD, 30KV or higher HV meter or probe, a variac, an adjustable position mirror (especially if you're working on color TVs), plastic alignment hex key and screwdriver... possibly a scope if you can afford or find a decent cheapie.

Nice to have but non-essential : scope, vintage capacitor tester that can check for leakage current at 450V or higher, one of those cheap $15 Chinese ESR/LCR/diode/transistor testers on eBay, Seco HC8-A in circuit horizontal output current tester, alignment gear (AM radio alignment generator which can double as a variable spare marker generator, a sweep/marker generator like a B&K 415, scope, frequency counter). A Blonder Tongue agile modulator is nice for finding a good channel on a tuner that has misadjusted channels and for adjusting channel slugs in tuners (a UHF capable model is good for testing UHF tuners if those matter to you, careful as some only do CATV IRC/HRC channels 14+ which are different frequencies from UHF).

There are a few more arrows in my quiver and some of these devices can cover for the absence of some of the others, but there are circumstances where one device is a pain and time vampire for a job and something else makes life easier to the point of being worth the money... A DMM can do the job of the seco for instance, but if you have a roundy color in the cabinet and you don't want to pull the chassis and solder to check/adjust the H output cathode current and don't want to do the dangerous practice of measuring the plate current then the Seco makes your life easier. The 107X analyst family has test pattern (and every other signal you could possibly want to inject for diagnosis) functionality but is not as precice or stable as a Solid State test pattern source...A modern digital scope with cursors that facilitate voltage and frequency measurement can do the job of a DMM and frequency counter (though if you fry the scope it is more expensive to replace).

You can go a bit more Spartan than my essential list but you have to use the equipment more knowledgeably and or work harder/longer for the results you want especially on some trickier to ID faults...time is money and you presumably have finite quantity of each so where to make trade-offs is a personal judgement call.