Ages since I've done any DIY mechanics but I think I'd mostly be buying tools as and when I need. That said, I would consider a reasonable set of sockets and spanners a good starting point.
As for the "pro" brands, I've a feeling my brother who was a mechanic felt that Snap-On were a bit of a racket/ over-priced over here (UK). His preference when he was in the trade was the French Facom brand. That said, at least at that time (I don't know the situation now) Snap-On was popular with other mechanics in the area.
Buy a repair manual. It should tell each tool needed for each type of repair.
Generally speaking you need to get a basic set of hand tools. Sears has plenty of sets to choose from. I would avoid the tool trucks for DIY stuff as they are really expensive. With that said if you were a professional I would recommend the tool trucks for most things.
I have been a mechanic for 27 years. At work I use mostly tool truck quality tools but at home I usually buy something cheap as long as it's not junk.
I'd say that if you are not a mechanic...not endowed with mechanical aptitude, forget the whole idea.
The very act of asking 'what tool?' tells me that you are totally clueless and should leave the repair work to those who are trained.
I could spend $150 on a simple repair at the local auto repair, or I might spent $350 buying tools that I will not need again or not for a very long time at least.
As an example, I might want a special washer....non standard size, not standard material. Can't buy one for love nor money. What tool would I need to make it? A lathe might be a good place to start. I could race out and buy one and all the various accessories that I would also need....
$3000 later assuming I have the skill to use the lathe safely and do know what accessories I need, I'll have my washer.
I could pay maybe $200 and have the thing fabricated for me in a 'jobbing shop'
I did all my own car repairs for the last 10 years or so, although I'm no longer doing it. What tools and supplies you need varies greatly by what kinds of jobs you're planning to do and also what make/model vehicles you're going to work on. Some jobs on some vehicles require specialty tools made just for that make or model.
Also you may be able to get by without certain tools, but the amount of additional time it takes to do a job may or may not be worth going without the tool. I.e. if you're planning to rotate your own tires or maintain your own brakes or other jobs that require frequent R&R of the wheels, an impact wrench will save a lot of time, but isn't absolutely necessary. Some chain auto stores lend certain tools for free (basically you buy the tool and they give you the money back if you return it within a set period of time).
If you pick up any Haynes manual, it gives a general list of tools in the front. Although I've seen some very strange things and procedure in Haynes manuals, things that are downright incorrect, at least for Subaru's. Alldatadiy.com is a good source of the genuine factory service info for many makes (some car makers offer that info free on their web sites but not all).
The most basic things needed I would say are a good socket set, wrench set, pliers set, and screwdriver set. It seems even the most basic of maintenance needs most of those. Beyond that you start adding whatever else you need, jack, jackstands, ramps, brake tools if you're doing brakes, etc. If you're working on a Japanese or Asian make you can generally get away with just metric tools. On a domestic I've seen a mix of metric and SAE fasteners on the same vehicle. Some makes such as Subaru use only certain size metric fasteners such as 10mm, 12mm, 14mm, 17mm, 19mm, 22mm and so on, which can reduce the number of wrenches/sockets needed, although if you buy a set generally you're going to just get all the sizes.