If you get a MIG make sure it's at least able to upgrade to gas. The difference is night and day.

I would say unless you are welding sheet metal or tiny delicate parts a stick welder would be fine, and it's also the best way to learn how to make a good weld.

A TIG is probably overkill for most of what you would ever do and is considerably harder to learn. Unless you'll be doing lot's of thin stainless, aluminum, copper, etc, it's really not something you should bother with. They are also a bit more expensive. It's essentially a plasma welder.

Welder Supply and Harbor Freight would be good places to look.

Welding brands are like asking about Ford or Chevy, Nikon or Canon... They are all pretty much decent, and it really comes down to what you wind up comfortable with and what color you love ;-)

Lincoln and Miller are both good base brands to start with. With BuzzBoxes (stick welders) it's pretty hard to go wrong either way.