Here's something I haven't seen mentioned yet, but make sure you have a safe place to weld. You don't want to burn the garage down trying to weld in a cramped space with flammable materials. If I weld in my garage, I make sure to clear the area, sweep (especially under shelves/benches where leaves/dust/etc. accumulates), and then do a 1hr fire watch. I prefer to have someone else there watching if I'm doing a tedious project (car exhaust, frame/roll cage work, etc), so that I don't miss something lighting up.
If you're going to weld outside with a MIG, know that you need to have a wind shielded area to do it in so it isn't blowing your shielding gas away leaving a porous weld (weak and ugly). For as cheap as classes are at community colleges, I'd definitely get in one to learn the basics/safety. Sometimes, they have supply houses that sponsor the college and will give you a deal on safety/packages.
If you go with a flux core wire feed (aka MIG w/o gas), plan on having a chipping hammer/wire brush at the minimum to clean slag. If you plan on doing a lot, a cheap 4.5" angle grinder with a wire wheel, grinding wheels, and cut off wheels will speed up most projects. Clean material and tight fit ups make for better welds. After a while, you get tired of throwing sparks and will probably end up with a sawzall/bandsaw to make a lot of cuts in project stock.
Background: took 18 months of community college night school to learn to weld then became an electrician. Trained for 3G/4G SMAW (stick "nuke" cert) but never took the test. Rarely weld at work, but am complemented when I do have to weld. Own a MIG for race car/general automotive repair.