I'm a total tool nut. There's times I'm at the store, and I don't ask IF I have that tool, I ask if I need ANOTHER of that tool.

Over time, I've broken pretty much every tool made, and I've learned to buy a bit more carefully. While Mac and SK tools are fantastic, I don't think it's realistic for everyone to be able to afford a kit like those.

That said, I've found that there are some ready-made kits that are fantastic starter tool kits. In particular, I picked up a kit from Home Depot that has been really useful, in a lot of ways.

It's this this kit from Home Depot.. Now this kit is missing a few important things, specifically tools for cutting, boring and measuring, so to this kit I'd add a cordless drill that uses an 18v or greater battery, a set of twist and spade drill bits from 1/16 to 1 1/2" by 16ths up to 1/2" and by 1/8" over 1/2".
I like Pull Saws, they are compact and cut well.
A good hacksaw and a set of blades is a must.
For measuring, the tool kit has a decent 25' tape measure, but a Try Square (6") would be a useful addition.

A good, stout prybar can get you out of a lot of problems.

Finally, you'll want a decent flashlight and a bin of fasteners - drywall screws from 1" to 2 1/2", some nails, some machine screws.