Here is some general info. on welding & cutting. Miller - Resources - Improving Your Skills
I use a mig , and a small o/a outfit in my shop. I can mig,tig,stick,O/A. I would probally try to learn to use a o/a before i bought anything else then try stick welding , then mig , and lastly tig .
Welding is joining of metals , usally done with a mig , stick, tig , o/a , Forge welding.
To cut metals is usally done with o/a, plasma cutter, various saws.
Chris