I would haunt Craigslist for a used torch/regulator/tanks. O/A is what you want if you have a safe place to wield fire - it can weld, it can braze, it can cut, etc. A MIG setup is great for putting a bumper on your old truck or fixing a railing, not so good for making bikes. Flux MIG is the worst of the worst, really only good for super sloppy non-critical work on thick materials. If you really get into building bikes you'll want to get some TIG stuff but that's prohibitively expensive for a first-time build.
I suppose my point is that if you're going to buy just one piece of welding equipment, or you're on a budget, an O/A setup is the way to go because you can basically do anything with it once you develop the skills. Read all the MSDS on the Acetylene, though - it is nasty dangerous stuff. Perfectly safe if handled with respect, though.
Just quick followups:
-Lots of old bike frames will have various nasty toxic compounds *inside* the frame to inhibit rust. They will also inhibit brain cells when smoked. Likewise many kinds of paint will liquify/run down into the weld zone. Do not trust that cleaning up some of the metal in the immediate area is enough to keep you safe! A good half-face respirator (you'll need to shave, c'est la vie) is ~$30.
-The little MAPP torches will not working for building bikes, unless you want to spend a small fortune on MAPP gas cylinders. Not enough heat to get big stuff like bike tubing up to temp. Those torches are intended for very small DIY plumbing/pipe sweating or burning wasp's nests and such. Don't waste your time/money.
-The MTBR framebuilding forum (
http://forums.mtbr.com/forumdisplay.php?f=142) has a ton of great info and fun folks (everyone from pros to first-time builders) and will give you tons of ideas.
-You might not save as much money (or any) as you think. This type of project often mushrooms in time/effort/materials costs quickly. Be aware of that going in and be ready to "enjoy" learning the hard way. :)
Seriously, hit me up if you need specific advice. And go read the FAQ at the MTBR site.
-W