What kind of bike do you have? That will drastically change what tools you need, specifically regarding bottom bracket, crank and cassette tools.
Personally, I buy them as I need them, but a couple things almost anyone will need to start out with:
Cone wrenches
Tire levers
Chain tool
Cable cutters
Spoke nipple wrench
Chain whip
Crank puller, to fit your bike
Cassette tool, to fit your bike
Pedal tool, to fit your bike, if standard tools don't work (they do on mine)
Generic tools you may already have:
Nice allen key set (so much nicer to have than one of those all-in-one sets)
Nice metric wrench set
Adjustable wrench that opens to an inch and a quarter or so (useful for everything from old bottom brackets to turning your cassette tools)
From there, you can kit yourself out with a whole pile of specialty tools, but that is the basics in my tool box that gets regularly used.
As far as brands, Park Tools is the standard SnapOn of the bike world, but i hear a lot of good things about Pedro's, and I've used some Performance brand stuff without issue.
Last edited by jefnvk; 10-14-16 at 09:56 AM.