I'm not a professional auto mechanic. I do have a large tool collection for homeowner use to fix things, minor auto work, to work on bicycles (I can do just about anything), to fix minor plumbing problems, work on electrical stuff (electronics and appliances), furniture kit construction, hobby stuff, etc. And I tend to go overboard if my finances and spouse permit.

But I've never regretted buying quality tools; on the contrary, as others have noted, if you buy something cheap, you'll end up replacing it after cursing. Only a few Craftsman tools are worth owning these days; you'll learn which are made by reputable quality tool makers, and which are (increasingly) junk. Stay away from Harbor Freight unless you are making an informed decision. I have only a few Snap-On ratchets and sockets, for special purposes.
I would recommend a set of the GearWrench Vortex pass-through socket wrenches, covering 1/4" drive and 3/8" drive equivalents, in SAE and metric, along with their set of insert bit sockets (hex, torx, etc.). That means you don't need short and deep sockets, can have enough to fix just about anything you'll find and do some work on a car. They're an incredible bargain and are very high quality. Two sets of Gearwrench reversible lever wrenches would be good, too.
If you need more sockets, you can get them later (over the years, I have acquired S-K 1/4" and 3/8" drive socket sets, as well as sets of older Craftsman USA-made sockets, and a slew of ratchets, but I have separate tool sets for bicycle work and general home use.
For screwdrivers, Wera Kraftform powerbit and insert bit drivers (various ones) and a set of Felo ergonomic grip drivers for times when the Wera aren't going to work out. Hex and Torx key sets from Bondus, in small and long variants (the long with ball-ends).
Pliers & cutters from Facom and Knipex (electrical variants and mechanical use). Micropliers from Klein, Xuron, and CHP (but I do a good deal of hobby stuff with them).
At least one Dremel rotary tool: I have an AC-powered one and their Stylus, with plenty of attachments and burrs. Eye protection is a MUST.
Woodsaws, a hacksaw, and a jigsaw. Two sets of files (regular machinist's files, and a set of micro files). Quality levels, squares, and rulers.
Several hammers! Some are all-steel, several Warrington-pattern hammers, framer's and trim hammers, dead-blow, soft-face, etc.
Drills, drill bits, and accessories (you may well need only one of the new 12V lithium-ion driver/drills, but you can get a more powerful battery-powered drill. A good AC-powered drill is always going to be handy.