There really is no point in going hog wild on expensive tools you aren't going to use.
For the most part, even if you use tools everyday in a shop environment its not cost effective to buy top of the line. Especially these days when the cost of tools is outrageous.
On the other hand, you don't want to buy junk either. I have nothing against cheap - providing its functional.
Take the cordless tools. They are great, very handy. But you mention wanting a cordless that you might someday use to change a tire. The price for a cordless impact that is capable of breaking loose lug nuts is around $400.
Seems like an awful lot to spend for something you might use someday. A $20 4-way will do the job just fine, or even a breaker bar with an extension and socket. Even whatever the manufacturer put in the car will do in a pinch - and that's free.
Now if you were changing tires several times a day, or even once a day without a decent air setup then it would be a different story.
But one of those cordless kits with 3-5 tools would be pretty handy around an apartment perhaps, and if you later move to a house they would be even more useful. I have several Ryobi tools that have been working fine for years and they are reasonably priced.
I used to have an expensive bosch cordless drill. The batteries died about a month after the warranty on them ran out. $135 for a new battery, $270 for two (really the functional minimum to actually use a cordless for any real job) for another $20 I could buy the whole new set again. Instead I bought a Ryobi set for less, and the batteries are $35 each, or for just a little more than the price of two I can buy another tool I don't have and get two batteries and another charger.
Once again, if you are building decks for a living it would be a different story.
Without knowing what you have already, what I would suggest is a 5 gallon bucket - or a 7 gallon if you can find one, and one of those bucket organizers. Worth spending the money to get a good organizer.
You can put an amazing amount of stuff in one of those, its easy to carry around and the tools are easily accessible.
Then you can fill it with reasonable quality tools and various whatnots.
Like a good pair, or better yet 3 pair of safety glasses - also worth spending some money on.
A good cordless light. The ones that come in the kits are ok, better than nothing, but a good light is extremely helpful in most situations. I like the monster led, the charge lasts pretty well, and they are pretty tough. Dropping it won't kill it, unless maybe you drop it off the apartment building roof.
Good multimeter. Lots of issues around the house are electric, same with cars - more and more as time goes on. Maybe one with a current clamp, or a separate current clamp, one of those little yellow outlet testers, wouldn't keep the meter or the light in the bucket though.
Plus all the various odds and ends that go with wiring/electrical - wire nuts, zip ties, electrical tape, etc....
Maybe get one of those flat divided organizers, good place to put the odds and ends. You could put them in the bucket organizer but they tend to hide in there.
In the flat organizer I'd also get a variety of common hardware. Drywall screws, 1/4" bolts/nuts/washers, that sort of thing. It will fill itself up pretty fast if you buy a little extra when you have to get something like that.
Various consumables - mechanics safety wire, duct tape, Plumbers tape (the stuff about 3/4" wide with holes every inch or so, comes on a roll) JB weld, pb blaster, silicone, anti sieze, thread tape, glue, hose clamps, fuses, etc.... Maybe in another bucket or a shelf somewhere - oh, blades and bits for the cordless tools - some of those in the bucket organizer of course.
Back to the bucket: Speed square, carpenter pencils, metal scribe, paint marker, Drill bits (decent bits are expensive), carpenter hammer, ballpeen, driving hammer (maybe), 3/4" cold chisel, center punch, pin punches, nail set, regular pliers, lineman's pliers, Dykes, wire strippers, vice grips (assorted), level, tin snips, chalk line (maybe) plumb bob, Razor knife, regular knife, serrated steak knife (great for cutting/trimming hose), screwdrivers, torx drivers, at least a couple tape measures, string/cord, line level, keyhole saw, Cresent wrench, C clamp or two, small rack of 1/4" standard sockets, small rack of 1/4" metric sockets (don't have to be great quality for around the house type stuff) ratchet, couple extensions, glass cutter, awl (can double as a scribe maybe), cats paw, small flat bar, medium pipe wrench or two, maybe a basin wrench but those type of fittings are becoming less common, caulk gun, kitchen sink.
That's pretty much a review of what I have in my around the house bucket (plus what I forgot), part of one shelf in my metal cabinet, and a nod at the hardware/consumables stash.
Not much of that carries over to the car repair, its a hassle to switch out the few tools that do so I just get cheaper stuff and leave it in the bucket, drill bits I went with a $30 Milwaukee set and leave them in there also.
Still, by the time you buy all that, even with non premium but decent tools you are probably around $1000, definitely more if you buy an expensive cordless set.
You may not need everything I've listed, and you don't have to buy it all at once of course, but I will guarantee you will use all of it if you do any kind of even moderate home repair, and you will be prepared for most anything of that nature.
If you still have money left to spend and you think you might need them, then a corded circular saw is way better than a cordless for anything other than the occasional cut here or there. 1/2" hammer drill is often useful, and perhaps a small grinder. Propane torch and some solder, maybe a soldering gun also - kinda depends on what you end up doing.
For the automotive stuff, I'd say get one of those kits. I've got a older craftsman set with a case I keep in the truck (along with a bunch of other stuff, lol). I haven't looked at the newer craftsman stuff, but from what I read here you might want to consider another brand.
The nice thing about the sets is they are portable, and with a case you don't need to worry about a tool box per se yet. They are generally somewhat well organized and its easy to tell if something is missing. I'd go with one that is mostly sockets and has some open space to put other stuff.
I've yet to see a set like that (around 300 piece give or take) that is very well set up for working on cars, maybe somebody else has a suggestion about a set I've missed.
From what I see they never have enough wrenches, 5 metric and 5 sae is guaranteed to drive you insane in a short time. The screwdrivers/pliers/whatever are generally not great quality, or what you functionally want, or the sockets skip around - also extremely annoying. So I go for the sets that have lots of sockets that don't skip sizes and add other tools as necessary.
For what you are doing, you don't need snap on or Williams or wira or any of the other high end brands. You aren't doing this for a living after all, and probably won't be. But if you end up making money doing it you can use what you have until you can justify spending that kind of money, at which point you can just leave the reasonably priced stuff in your vehicle for emergencies.
Also, if you run into the apartment for a drink of water, or to go to the bathroom, or to get another tool or whatever and you come out and a bunch of tools has walked away on its own you're out a couple of hundred dollars instead of a couple thousand or more.
Plus, the more expensive a tool is, the more likely it is to walk off. Not many thieves are going to steal your beat up looking $5 harbor freight screwdriver, but they are going to be way more interested in your $300 set of snap on screwdrivers.
I've been using a set of harbor freight screwdrivers in a shop setting for 3 years now and other than looking chewed up they still work fine. Unfortunately the last time I was at hf they didn't have the same kind anymore. They are the orange/black and green/black ones that sold for like 2 or 3 dollars each. I've got 5 standard and 4 Phillips, so for $20 some odd dollars they are hard to beat.
Maybe one of their aluminum floor jacks, pair of jack stands - steel floor jacks are heavy to tote around. Like I said, just depends on what you want to do, or end up doing in the future. HF does have some ok stuff, but also a lot of junk.
I've tried to keep my suggestions realistic from both a cost and utility standpoint. No point in spending thousands of dollars on stuff you may never use. The stuff I've listed is all useful for any sort of basic work right now, and useable/handy no matter what direction you go.