Be ready for a flood of responses. There's standard tools of the trade, then a mountain of things that are of personal taste. Lots of opinions abound.
I'll start with a simple basic maintenance kit for you. I may miss a few things, but you'll get the idea.
Nut drivers. Get a 1/4", 5/16", 11/32". You'll use these frequently to remove playfield plastics, light socket (from below), other playfield parts, etc.. If you want to splurge, get both magnetic and non-magnetic. Experience will tell you why this matters.
Screwdrivers. Flat head, phillips.
Wire stripper, soldering iron, solder. Wires break off - learning to do a quick solder will save you headaches and cash. Watch a few YouTube videos on soldering if you need help.
A basic multimeter. So when things don't work and your Pinball friends here tell you to check something you'll have the tool for basic checks.
Small level (like 8") and an inclinometer. Every time you move your pin you'll want to level it and set the right angle. Some pins come with a built-in angle level, but don't count on it.
Novus #2 and lint-free cloth (you don't need #1, but you can get it if you want for quicky cleaning). Don't buy #3, too harsh. Opinions abound on it's uses, but most will agree it's your standard for playfield cleaning.
Glass cleaner and a good supply of paper towels. I like Stoner glass cleaner. Does a great job and dries without streaking. And it makes me laugh when I ask the wife where my stoner is.
Bulbs: #44 and #555 are used a lot for most playfield, insert, back box applications. Also #89 and #906 for flashers. All bulbs burn out, and you'll go through these like candy. Consider LEDs down the road after you gain some experience, and open your wallet more for the hobby as they will get expensive, particularly when you want to replace every bulb on every machine you own (because you will buy more than 1 )
A spare supply of new pinballs. Nicked pinballs damage playfields.
Good luck and enjoy the new hobby.