Oxacetalene welding - Uses Oxygen and Acetl. gas to produce hot flame. Then uses filler rods with flux for welding or brazing fed manually. As there is no shielding gas, it can't do Aluminum (can do aluminum brazing) or some alloys. Takes practice, can be difficult. Brazing is much easier.
Gas Tungsten Arc - GTAW or TIG, Uses electrical arc torch with a shielding gas. As weld is shielded, it uses filler rods they don't need flux and are fed manually. Can do almost any metal with the right filler rod. Non-ferrous metals require AC. Hardest to learn, but can produce the best welds.
Gas Metal Arc Welding - GMAW or MIG. Uses a gun that feeds filler wire automatically. Wire arcs against the metal and melts creating a weld pool. Gun uses a shielding gas to protect weld from air. Can do steel easily. Non-ferrous metals can be done (Alum.) but not as good as TIG. Easiest to learn and is fast also only needs one hand.
First, you need to decide the metals and your budget. Gas can be cheapest, but hard on small stuff and alloys. TIG is the most expensive but can do anything.
For sculpting, I probably would do gas brazing as it is easy and can mix metals well (notice sculpting class mentions brazing.) You can braze with MIG also.
I have done all 3 (and arc/stick SMAW). If I were to choose only one for my work, it would be MIG. But for sculpting, I would do gas brazing as it is easy, runs lower temps and plenty strong enough.