*) Sweep generator aka. 'Wobbulator'. I have to disagree with PA4TIM here. A linear 10.7Mhz +/- 1 Mhz sweep generator is almost mandatory for working on FM receivers, preferably with some form of logarithmic detector. The dark secret here is that the original factory service manuals from the fifties and sixties are flat out lying here. They were written with the intent that the service personnel wouldn't have access to a sweep generator, so the simplified technique most frequently given, is meant to at least 'blow a hole though' to make the radio generate some form of sound.
However, if you are really looking to maximize the audio quality, then the 10.7MHz IF absolutely needs to be swept and properly aligned. Things like Grundig's reflex IF and the monster 8-12 tube models pretty much requires this. This count double, if you intend to extend the IF bandwidth to today's standard. I also wish anyone good luck, who would attempt to align one of the modern receivers from the 80'ies without a sweep generator.
Same sweep generator will also come in handy, if you have to repair or align things like the domestic receivers from the fifties with permeability tuned variable bandwidth 455 KHz IF, intended to maximize performance on SW reception.
*) Tube tester: I honestly wouldn't put this high on my shopping list, as long as you are working with domestic receivers. The designers working on these radios knew what they were doing, and as a result these radios were usually designed to work splendidly even when the tubes had lost a fair amount of transconductance.
Also, at least for mains transformer equipped receivers, the heater/cathode leakage test doesn't really mean anything. Many tubes in these will have nearly zero volts between the heater and cathode, so a minor leak is completely unimportant.
So trusting the tube tester when the tubes test bad is a mistake in the general case, you will discard way too many perfectly serviceable tubes. It should be considered the rule rather than the exception, that all the tubes in an old domestic radio work. It is the passive components around them, which fails.
Conversely, even if a tube tests good, then you still have to thoroughly test it in circuit. The triode oscillator in the conversion tube is a famous example, particularly if the receivers has SW bands. Additionally, this particular triode is very, very frequently completely dead, but just this half of the converter tube. This happens, when the receiver was mostly used for FM reception, very common here in Europe, where power is turned off to the oscillator (only used for AM/SW reception). So the triode dies from having heater voltage applied without HT, causing cathode poisoning. Yet if you only want the receiver to receive FM, you can simply ignore this issue, and keep using the tube.
Eventually you will know which tubes tend to be trouble makers, either inherently, or due to their position in the schematic. For instance the UL41 audio amp pentode, used in radios with series connected tube heaters, is a notorious candidate for H/K failure.
The reason why high quality tube testers were made originally, was that many high end circuits, like those found military, communication or video equipment, actually are quite sensitive to for instance both heater/cathode leaks and low transconductance.
Low quality tube testers, like those found in your local repair shop back in the day, are largely useless marketing machines, meant to increase revenue for the tube manufacturers.
*) Capacitance/inductance meters: Never had much use for those in connection with restoring domestic receivers. The inductors and high frequency caps rarely fails, except when there is obvious, mechanical damage.