Turntable maintenance is fun for me. I have slowly aquired a tool box of items that I have needed at some point over the years.
Number 1 item is a good light source.
Number 2 is a pair of +3.25 reading glasses for up close work.

A soldering iron and volt meter.
Different oils and syringes, isopropyl alcohol and charcoal lighter fluid for cleaning, lots of q-tips and paper towels, blue tack.
Of course, a jewelers screw driver set, needle nose pliers and a small wrench and ratchet.

I found a cheap 2X10 microscope at a garage sale I use to inspect styli and really tiny stuff, comes in handy some times.
A digital scale is a must and a strobe light is good to have.
You'll find out what you need by reading stuff on line, little tricks that make it easier.
Rubber bands, painters tape, super glue, pipe cleaners, bubble level, paper clips, exacto knife, are all in the bottom of my tool box.
Edit: also, sign up at VinylEngine.com and HiFiEngine.com for free manuals and schematics.