My eyes are fine so tend not to have a microscope on hand for most things short of full bore BGA. I have some magnifying kit for the edge cases where I might be trying to spot corrosion but otherwise I am not bothered by having a mantis or whatever around.
Soldering.
Hot air is pretty much an essential these days, though I am content enough with whatever half decent aoyue one is out there. I prefer my hot air made in the station rather than the tip but that is preference.
I mostly deal with a firestarter iron from mercury. Have a soldering station I can set heat with, and a variac/autotransformer if I really cared for the firestarter, but that is usually more useful for determining melting point of plastics.
Have used the fancy tips. Don't think they make a lot of difference for my purposes, at least outside of having a hooked tip for use inside vehicle looms. That said a decent spade/flat bit, well tip and horseshoe bit can have perks.
Have been tempted to add IR to the pile of gear but can't really justify the bench space.
Have a lighter fuel powered portable one, don't think it has been charged in a long time. Not been tempted by any battery ones as most times I go anywhere to fix a vehicle I have power (or they dragged it to me) and the simple firestarter fits in a bag. Do have an older mercury firestarter at a client's though.
Inherited a bunch of beefier ones but that is less PCB repair and more solder as mechanical device repair.
Flux is flux for the most part. Have paste and squirty forms.
Solder. I have a nice collection of glorious leaded solder of various sizes that I pick up from wherever I find it (usually old tool kits at car boot sales). Paste and balls for BGA I tend to get in as I need them -- paste being more useful for me when I am building out PCBs which I try not to get involved with.
Wire. All various colours, nature of strands, crimp connectors and whatever else, plus the box of scrapped cables that have saved the day many times. Tend not to have the greatest range of high temp stuff unless I am involved with things that need it for real (industrial kit tending to warrant it more than installing a new wire.
All the colours of electrical tape.
Some heat shrink. Do have some really long stuff for fixing motorbikes as well but that gets expensive.
I do have a glue gun/hot snot. Quite useful for filling and stabilising things (laptop charger ports most commonly where no replacement exists so I just whack in a generic replacement and sort the charger end) when epoxy is a bit too extreme.
Solder braid/wick is what it is. Have thin and fat stuff.
Have a cheapo solder sucker.
Don't feel particularly compelled to have dedicated desoldering gear.
Few solvents. Mostly acetone and alcohols that don't leave anything behind. Plenty of electrical grade contact cleaner, don't tend to spring for the fancy "can use this on live gear" flavours.
I do have some clear nail polish to do a poor man's conformal coating if I think it necessary. 99% of its use is for when I take a slice out of one of my finger/toe nails and need to give it a coating while it heals.
Have some superglue for fixing cases and occasionally sticking down a part if the hot air+solder = it moves to the correct location.
Have various flavours of rotary tool. Don't have the most use in PCB repair but when I do there is nothing quite like it.
I do have various drills but tend not to have to drill screws out. Such things instead being more for making PCBs.
Do have hand reamers/tapered reamers/repairman's reamers though. Wonderful things for enlarging holes in most things actually, especially plastic and thin gauge sheet metal though.
I can see having a fancy spudger but I mostly don't and instead have the cheapo plastic and basic metal ones.
I do have a nice suction cup, however the basic ones with keyring pulls on are not so bad for most purposes.
Usual collection of metal, wood and plastic picks. It is worth getting a plastic screwdriver to adjust sensitive potentiometers (granted I can't remember the last time I did a POT tweak for a laser and most of the time it is useful for adjusting my oscilloscope).
Screwdrivers. I try to get security version standalone ones for everything rather than a bit set (though I have several of those too) as modern stuff has a nasty habit of having deep holes using "security" versions of whatever already uncommon bit they are using that won't allow the chunk bit holders down.
That said for starting out decent flat, cross (do note Japan has its own flavour of cross head) and (security) torx get most things done, chuck in apple, nintendo or whatever your focus is likely to be and yeah. That said a basic "non standard" bit set is worth having and does not cost a lot.
Don't know that I would have an electric one for anything other than TVs (and for that I have a giant yankee bit screwdriver I rammed a normal screw holder down in, reviled tools for many but wonderful for me when doing this sort of thing) and domestic white goods which mostly takes you away from PCBs.
While it is generally heresy in the UK (outside of mains work then if you can solder it then you do so) I do have a reasonable collection of crimp tools and crimps. Can get epoxy filled things but save that for the occasions that truly need it.
Ultrasonic. I have such toys. Can't say I use them that often for PCBs but also tend to shy away from the "I spilled coffee" set, or if I do then replacement PCB is usually cheaper for while I can fix your apple product I don't cop to that too often.
Wonderful for sorting clogged things with small holes for engines though.
Scope wise. Nice to have but 95% of the time a basic ohms, diode, volts, continuity meter and maybe ESR meter* (though for that you can probably get away with one of those component ID kits rather than straight up). While for learning electronics then any scope with at least two channels will do then for repair I would say one with the barest whiff of memory will be necessary -- tracking behaviours relative to other points during power up/off/running is a fairly key diagnostic.
Power supplies are mostly dumb things for me but if you want one that tells amps drawn that can work for diagnostic flow.
Do have a signal generator but not sure I have ever used it in a repair. This might change as time goes on and I can see a path.
*while I have what I presume is a victim of the capacitor plague on my bench as I type this then that is coming somewhat to an end and visual does most of what you need there. There have been a few subtle ones though and non electrolytics that fail so maybe.
