Don't overlook running a separate service to the garage. No need to disturb the house that way, and lots of room for more breakers.
That's also a good time to have a security light installed if the power company adds a pole.
As to machines, the previous suggestions are all good.
I favor a basic stick welder for a first welding machine because they are versatile, tough, simple, and easy to work with. DC is worth the extra cost.
Practice, and practice more. It's worth it. Bend lots of practice specimens.
Also, check out Weldingweb, the Hobart welding forums, the Miller forums, and Shop Floor Talk for useful info.
EDIT:
Avoid arc gouging with light duty machines. It's rough on them. We use a Lincoln 600 at work just for the purpose.
I got a torch instead for cutting and gouging. If you don't plan on welding often, consider getting a oxy-acetylene setup before getting an electric welder. You can cut, weld, heat, and braze with it, and can save money cutting by using propane (requires a different cutting tip).
