First off, let me say, I'm a self-taught welder.
There are certain things that you REALLY need to see/hear a skilled welder do ONCE (or until you "get it"). For example, a lot of guys talk about how a weld SOUNDS as you're laying it down, mostly described as "frying bacon". Until you "hear" what a good bead/bad bead sounds like, this can be difficult. Once you start welding, you will wonder how you ever lived without it in your shop.
Second, let me also say, your $2K budget is excessive. If you can reasonably say you'll only be welding steel, then the price comes down dramatically. I do a LOT of wrenching/fabrication and have seldom needed to work aluminum. A good entry level welder would be like the Miller 211 or even a Hobart 187 (they are the same company).
http://store.cyberweld.com/mi211migwewi.html
http://store.cyberweld.com/hoha187migwe.html
Now if you WANT to buy the LAST MIG welder you'll need as a hobbiest, then you would step up to the Miller 252, in which case your budget is looking a bit more reasonable.
http://store.cyberweld.com/mil251witmet.html
Helmets: you only have one set of eyes. In this case I like to use the old Bell Helmet ad from back in the day: If you only have $10 eyes, then only use a $10 helmet. Get a quality autodarkening hood. I like my Miller, Hobart makes a cheaper version too.
Resources: I can't believe that we've come this far into it, and nobody has mentioned Weld Talk... It's the Garage Journal for welding...
http://www.hobartwelders.com/weldtalk/