You basically need everything that isn't a game specific part. It will eventually break no matter what it is. And with 10 games you'll see plenty of stuff break. For some games you need game specific parts for backup such as Funhouse/Road Show. You need extra eye plungers and the jaw gear as well as the little coils in case one burns up.
Things you need that are often overlooked are coin door parts and coin mechs. You'll have coin mechs that are finicky and sometimes you just need to swap them out.
It is also a good idea to have some Lexan (polycarbonate) on hand so you can make plastics that break and cause ball hangs. Or to cover an area where a plastic part is missing or broken. You'll often not realize something is missing until the game is on location and you get hangs.
It is also a good idea to have metal on hand you can cut and bend to make brackets, etc.
Have sheets of Mylar so you can protect areas where you are seeing wear.
Have extra playfield glass. Do this long enough and you'll have one break.
Make sure your scoops and troughs are solid without broken welds. If welds are broken, get them fixed before you put the game on location. Last thing you want is a scoop not able to eject a ball or throwing the ball and damaging the playfield.
Some odd things I've needed and was glad I had backups: lockdown bars (welds give out), flipper base plates, shooter rods, external shooter springs, leaf switch parts and contacts (both gold and tungsten) so you can repair or make your own switch stacks (PBR sells parts).
Some other tips: Check that your games are properly grounded. On WMS/Bally games BOLT DOWN THE HEAD, don't rely on the latch on the back. If you have playfield glass that has large chips on the edge, don't use it.
Some tools I'm glad I had: circuit breakers with fuse attached (see pics below), rivet press.
This was going to be a short, quick reply. So much for that.
Some examples:
DSCN1092_(Custom)_(resized).JPG
sandman_(resized).jpg
DSC_7366_(Custom)_(resized).JPG