Wrenching on your own bike is awesome and definitely something you will get a lot of satisfaction out of. Here's my advice:
Like the others have mentioned, buying a kit and a stand are essential. For the average home mechanic, a cheap kit like the one from Performance Bike or Nashbar wouldn't be a bad place to start. For frame tools like taps and reamers, Ice Toolz makes a decent set for the price.
Nashbar actually makes an exceptional budget headset press, a little ugly, but works just as good as Park IMHO. One tool that I especially love is the Pedro's Vice Whip, it's a chain whip built into a pair of vice grips. Expensive, sure, but it works awesome and is worth every penny. My portable tool of choice is the Crank Brothers M19.
Also, keep an eye out for Wrench Force tools; they were made by Snap On for Trek's brief venture into shop tools. Sometimes Trek dealers will have a stash of them hiding somewhere, or they will pop up on that auction site. Last month, I landed on a bunch of NOS WF combination wrenches in all sizes for $1.25 each... again, these were made by Snap On...
As for stands, I especially like the Park PRS-4OS bench mounted stand, although it is pricey, it gets a ton of use in my home shop.
Cheers!