most aircraft are in imperial so your metric stuff from cars will not work.
1/4 drive shallow and deep sockets as well as universal/swivel sockets. all 12 point
1/4 drive extensions with the knurled bit on them
ratcheting screwdriver. I have the long and short T-handle ones that work better for me
long spline drive wrenches. there are 2 you will need one has 1/4 and 5/16 and the other has 3/8 and 7/16
as for the rest. you can find a lot of good stuff on Amazon.
Mastercraft maximum wrenches are as good as the snap on stuff but 1/25 the price.
for wrenches you will usually use 1/4 to 1 inch in size.
for pliers, princess auto/amazon are your friend. I wouldn't waste my money on the snap on truck with those.
as you get more experience in your career, you will decide what you need and what quality you want to buy.
as for a box get one you can use as a work surface. and the largest one you can afford.
this should get you started. it's probably going to be about $1,000 for the tools and box to get you where you don't need to borrow stuff anymore.
If you've been around automotive - You should have what you need to start out with...decent 3/8 and 1/4 drive sockets, wrench set including the oddball ones like 11/32 that are not in the basic sets. Screw driver set, standard hammer as well as a soft face and a dead blow - maybe 5 lb. You will always be adding to it - but that a decent start. Make sure you use decent quality stuff and not the cheapest you can find. It's great if you have a lifetime warranty for tools (I'm talking about the cheap stuff) - but if that wrench breaks at 2AM and the plane leaves at 6 - that warranty doesn't mean squat.
It all depends where you will be working too. My first few years I also had to but some basic sheet metal tools. And heli's may require some different stuff as well.
One word: KNIPEX