There are countless options elsewhere online for electronics lab on a budget type setups. I did have an article on electronics in the works but nailing the suggestions for a setup here is something I have to finish up.
Granted auyoue or whatever it was hot air station. They are not as nice as some that might use them every day will go in for but mine have variously earned their cost 10 times over during the course of random days, never mind the years I have used/owned them.
Wedge or well tip soldering iron or replacement tip for one. Chances are anything with a wedge tip will be fine out of the box, there are decent firestater irons rather than having to jump into the temperature controlled efforts.
Leaded solder, preferably with resin/rosin core and on the thinner side.
Braid/solder wick
Flux
Solder sucker.
Kapton/aramid tape.
Electrical tape
Abrasive tool (tile cleaners can work but they often have chemicals in you don't want, simple fibreglass pen is good stuff) or I guess you could deal with a scalpel, and you might want a scalpel if you are cutting traces for something.
Contact cleaner.
Basic my first multimeter should be fine (no need to jump right into fluke or anything silly). If you want to step it up slightly into something with a bit more accuracy and a continuity beep test then that would probably be my first choice (assuming you are not lumped with a cheap tool shop soldering iron).
Epoxy, superglue and hot glue can all fill or protect things that might need protecting. If you only need a thin layer where you scratched off some mask then clear (or whatever your chosen colour) nail polish is good stuff and actually what the high end pro custom nonsense is.
Depending upon what you are doing (mod install is different to repair which is different to analysis, or if you prefer there is a reason I did not ponder oscilloscopes in the above bit).
Also the search bar in the top right of the page can restrict to thread only searches if you can remember some phrasing.
