Hi Kyle,
Check this link for a starter airbrush setup.
Airbrush Starter Set It's not that cheap, but it comes w/ a TON of stuff. Perfect for a beginner IMHO. Comes w/ paints, video how-to....all sorts o' goodies. You're going to be spending at least that much if you put together the pieces this starter kit comes w/ separately. That being said, only you can decide how much money you're willing to spend.
I started out painting minis as well! W/ a little practice, you can include the airbrush in painting your miniatures. As for the "beginner" link you posted, painting like that can be accomplished by a beginner to intermediate, but I would definitely recommend you practice getting control of the airbrush before you tackle something like that. As for "how long", well, that depends entirely on you and how much practice you put into mastering the brush. Much easier to approach a complex airbrush job w/ the confidence you know exactly where the paint is going. CB and Danno hit it right on the head...this hobby ain't cheap, and you would be much better served spending your cash on good equipment before you tackle more expensive kits and such.
On other thing, as CB said, it's only paint. You can keep working it until you get it right.
Rick