Look for a tool library near you. See if you can borrow some from neighbors. You'll get the hang of doing jobs, and what good vs bad tools feel like.

Going against the spirit of the post and recommending nothing.

Start your project. Hit the store for what you need. Rinse and repeat.

Once you get a feel for what's useful to you, keep your eye out at the flea market, garage sales, whatever.

Here are a couple of items that I wish that I had picked up earlier. They are not required, but they greatly simplified my life.

• headlamp: Trying to balance or prop up a flashlight while working used to result in so much frustration.
• tin sheers: I love these so much that they have replaced scissors in most day-to-day applications
• flexible drill bit extender: So many screws are in places inaccessible to a drill body. This inexpensive item solves that problem. Magnetic wristbands: Keep those screws and bits from getting lost.
• level that is at least 2ft long: I really appreciate having a level that can span two studs (16")
• precision / mini needle nose pliers: I don't need them often, but when I do I am always happy that I have them
• painters tape: I am surpised how often I use painters tape for all sorts of applications

Harbor Freight is your friend. Their cheap tools can suck and may break with repeated use, but that's almost a feature.

If you use a tool often enough that you break it, then it's worth investing in a quality version of that tool. If you don't use it often enough to break it, you can get by with the lower quality.

If you've got sockets, wrenches, pliers, and screwdrivers you're 90% there. Get an impact driver, you can use one for pretty much anything with the right bits. I buy DeWalt or Milwaukee power tools in the US personally, but it doesn't matter much. You won't be using it all day every day, dropping it off scissor lifts, etc like I do.

A good set of jacks will go a long way. And start collecting flashlights.

Electrical meter

Tire air gauge

Tire patch kit

Air pump

Brake reset tool (forget exact name, I paid $10 and it pushes the brake piston back in when installing new brake pads)

Tire thread measuring tool (know when you need new tires)

Battery tester (test how many cca remain)

Battery acid tester

Radiator coolant tester

Distilled water to put in battery

Coat hangers (metal hanger can be cut and bent to hold things such as the brake caliper)

The tire patch kit saved me a few weeks ago.

In addition to the torque wrench, a breaker bar is helpful. You didn’t mention it but Allen wrenches are vital.

Also, all hail Harbor Freight. Great place to get cheap tools. If you don’t think you’ll use a power tool more than once a year, they have some great cheap shit too. They do have higher end power tools, but they have frequent sales so I would wait for one of those.

Otherwise, other tool choices come down to the type of work you’ll be doing. I do more wood stuff personally, but you sound more like a metal guy