Some good info here:

http://collierwelding.com/tech/welders/

And TONS of info here:

http://www.millerwelds.com/education/library.html

MIG is short for metal-inert-gas but this has been replaced with GMAW (gas-metal-arc-welding). TIG is short for tungsten-inert-gas and is more correctly GTAW or gas-tungsten-arc-welding. Both use Direct Current (as oppposed to Alternating Current). The major difference is that Mig uses a wire-feeder to transfer metal to the joint to be welded and uses Reverse-polarity. Tig uses a torch which holds a tungsten electrode (along withan inert gas-usually Argon) which provides heat to melt the base metal and you have to manually feed the weld metal. Tig also(generally) uses Straight-polarity in the welding circuit.
I would say it is easier to learn to mig weld.
You can weld with an oxy/aceteline set-up, but it is harder to learn than Mig welding.
You might try going to a welding supply store and ask them to define the differences in the welding processes and they may even be able to demonstrate for you if you are serious in buying the equipment.
Mig is pretty good way to go if you are a do-it-youselfer as it is really easy to learn once the machine is set-up correctly.
Hope this helps.
Be well.

By all means, visit the Miller site as reccommended. You may also want to purchase "Welding Essentials" by Marlow/Galvery. This text has easy-to-understnad information that is great for the novice.

As for learning, it's practice that is the key. I can't think of a better way to begin than by mastering oxy-acetylene welding. Things tend to happen more slowly, so you have a better chance of seeing the errors of your ways before the hole appears in your work! It gives you an oppotunity to become familiar with the way metals behave when heated, and some insight to the metallurgy, which you WILL need to know to weld successfully. If you get serious about this craft, you'll want a good oxy-acetylene rig anyhow, so why not first?

Yep, MIG is the way to go for what you want to do!