start with Mig, stick and Oxy and progress to tig, dont buy a unit until you really have to and maybe wait until you have tig down to a good point and can afford to start doing it at home...
I did three courses or metal arc welding at Tafe, included stick, oxy and mig and finished off with some tig... it helps if you can progress through the different welding techniques, there is alot of info to learn as far as filler types, different heats and joint types...
Dont expect yourself to able to be a good tig welder by the end of some short courses though, it takes practice, even mig welding takes practice to get nice pro looking welds, and just because it looks good doesnt mean its strong... so practice practice and practice....