Dealership tech with 25 years of experience, now service manager for an Asian import store for the past 4 years.
Do not spend any money on SAE sockets or wrenches. Especially to start. Even Domestic brands stopped using SAE sizes in the 90's. There was some years of overlap where you might need both sets, but none of my techs now have any SAE sockets or wrenches. If you run across something specific you need just buy that wrench, ie one 9/16 don't buy the set. Most of them will sit in your drawer taking up space. Some are the same any way. a 19mm and 3/4 are interchangeable, as are a 16mm and 5/8 and 11mm and 7/16, 8mm and 5/16 are all the same.
Also definitely look into less expensive air tools, but that air ratchet you listed will stay in your box, or get thrown away. It won't have enough power the break any bolt loose, and most of the times even if you break it loose first it won't have enough power to un thread it the whole way, and if you use that air ratchet to break it loose by hand, the head will be junk in days. Save your money until you can buy a good one.
A small impact driver, like a Milwaukee 12v will be a lifesaver if you are taking dashes apart, etc. And I much preferred them to anything Snap-on had for that kind of job. And that's something where bigger isn't better. You don't need an 18v impact screw gun to take all the small 8mm and 10mm bolts, screws, torx screws etc. 12v stuff is fine.
In fact a lot of my guys use the new electric impact ratchets too. and the 12v version of them is fine about half the time as well. so see if you can find a package deal on them. Impact driver and ratchet, 2 batteries and a charger 200(ish) A good air ratchet is going to cost you 300-400 bucks for one that you will use and be usefull to you.
Lastly don't spend anymore money than absolutely possible on a tool box. It's not full until you have to shake the drawers to shuffle the stuff around to get them to close. A tool box will never make you any money. It only holds your tools off the floor. Any shop you should want to work at, you shouldn't need to worry about super duper security anyway. You should only need enough security to discourage guys from "borrowing" something when your away.
I've always worked with guys who never locked their box, or never put all their tools away. I promise you, you will lose more tools to forgetting them in some car you are deep into a job on, than other tech's stealing them. Unless you are working in a really crappy shop. I have spent all my career in large (30-50+ tech) shops in a major metropolitan area, and actual theft between techs was rare. Guys will "borrow" borrow stuff and forget to put it back. Because everyone borrows stuff, no one will have every tool they ever need for every job. SO you just don't want them borrowing stuff when you aren't there.
But you will need to borrow, so always return stuff right away, don't make the guy come looking for his tool. Always ask, even if that guy has loaned you that tool before. And keep track of what you borrow, if you borrow the same thing, several time a week, that needs to be your next purchase. But if you borrow something once, don't waste your money.
I have one of those monster tool boxes, 8ft long, 6ft tall, and it is slammed full of tools from 25+ years of working on cars. And I occasionally still needed to borrow something, I just made sure to be gracious when someone needed something I had.
Lastly if you make this your career, you will never stop buying tools. The manufacturers seem to constantly come out with some new shape of torx head, or or some new gigit to adjust tie rod ends, etc etc. not to mention diagnostic tools that never stop evolving to keep up with the huge technological increases every year to maintain emissions and fuel mileage standards
