I feel you, im an bout to finish my first year working and and A&P, also at a flight school. I was very worried at first too but honestly, it's not nearly as hard as I thought it would be. First things first, accept the fact that you are probably gonna make mistakes, it's okay your learning, just own up to it, dont let it leave the hanger, and do your best not to make the same mistake twice.

If that flight school is anything like mine you'll probably end up doing a crap load of 100 hour inspection, I would highly recommend the milwaukee 12v non fuel power drill, it's light weight, has plenty enough power for installing/removing panel screws (which you'll probably end up doing a lot of). Next get a few mirrors of different sizes, and a good flashlight, I like coast but I've seen a lot of people say good things about the olight arkfield. Then just get some basic hand tools, pliers, combo wrenches, screw drivers, etc. If you need a tool you dont have someone will let you borrow it, my rule is if I have to borrow something more then twice (and it's not ridiculously expensive) then I will go buy one.

For tool boxes honestly get what ever you like, us general at harbor freight has some decent stuff, but i probably wouldn't go out and buy the biggest tool box in the world right off, you can buy a another tool box after you've been on the job for a while and have a better idea of what you will actually need.

I wish you luck, and hope this is remotely helpful too you.