I was a mechanic for 5 years through independent shops and Honda dealerships. 4 Certificates and an associates in Automotive Technology.
As said above, you'll always be getting more tools. What I recommend though is not what you buy, but HOW you buy. Don't cheap out on your every day, every car type tools. Impact sets, sockets, extensions, prybars (for safety) are things you shouldn't cheap out on. The tools that you buy for one-time jobs are not exactly where you want to spend high end money. There are exceptions of course.
Take advantage of the school discount!
When I started in a tire shop, I used an impact all day every day, and sockets galore. I got top of the line with warranty, because those kinds of tools are essential and need to be durable. The big cardinal sin in a shop is borrowing tools. If you have to borrow it more than once, go ahead and buy it. DO NOT think its cool because a coworker just lets you borrow it. He might not speak up, but mechanics hate that! Some will straight up refuse after you get your first paycheck or until you put some time into the shop.
I have a thing where when I lose or break something like a cheap socket, I replace it with a higher end part, not the whole set. You're not going to break all your stuff, but more likely the things you use regularly will go first. Don't get discouraged when looking at experienced guys' boxes. They've accumulated thousands of dollars worth of high end tools over an extended period of time. Most of them also are still making payments on a lot of that!
Invest in anything to make your job go FASTER and easier. Work smarter not harder. Because in that industry time is money and it can be very stressful when on a deadline.
For example, I bought an electric driver to zip airboxes, splash guards, accessories, interior panels etc off in seconds, that frees up time that I need to spend on the bigger repairs or the work that needs to be timed consistently. Doing things like that by hand will kill your time. Also buy things that help your agility in the engine bay. Things like pivotal extensions and ratchets. Feel free to PM me if you have any questions and good luck to you! Always good to know people are getting out there in the field!