Are you wanting to go into ga or commercial? GA will require a lot more tools of you.
Common metric on GA aircraft is pretty much only on the lightweight alternators. No real reason to buy metric until you find out what your working on. I'm halfway betting that I could go and look at the wear on my sockets and tell which sizes of 1/4 and 3/8 drive to buy. My 1/2 drive only really sees the 7/8 deep for spark plugs.
Needle nose, duckbill, side cutters, and safety wire pliers would be bare minimum. If you can add a pair of the small knipex plierwrench's. They have a million uses, and are excellent on an fittings.
Standard combination wrenches and a decent set of angle wrenches, I started with tekton angle wrenches and never had one spread. Upgrade when you get some time and money under you, they are stupid expensive.
Flashlight and a headlamp, buy what fits your budget. I have a rechargeable led lenser headlamp and a rechargeable streamlight flashlight. Nice to not have to keep batteries around.
If your going to a shop that will require some fabrication.
-Air drill get a palm sized drill yardstore.com sells the texas palm drill which looks a lot like my sioux but a lot cheaper.
-An automatic center punch
-1/8 and 3/32 pin punch
-Cleco pliers (nothing worse than running cleco's with needle nose, those bastards fly)
-Steel rules and squares, honestly some of my most used tools.
-Hammers ball pein's and a deadblow should get you
A lot of the tools you need depend on where you get hired. They generally will give you a list at your interview. Stack a lil money back so you can fill in a gap if you have to.
Don't worry about starting out with big brands, the way the industry is going for the commercial and manufacturers, privately owned tools will be going away anyway. If you end up in GA be prepared for an intimate relationship with your tool truck driver or whomever you mailorder your tools from.