Go visit a few bike shops. They'll be able to help you out by suggesting bikes that fit you and your riding style. On that budget, you should be able to get a good bike from a shop.
Giant is pretty good (or so I've been told) in terms of bang-for-buck. I got mine (2009 Giant Avail 3) for about $800, and I love it. When you look at bike specs online, look for the rear cogs (or cassette, depending on whose website it is). A larger second number generally means it's better for climbing. The "local" bike shop I visit when I'm at home (not the one I bought my bike from) has a little guide which explains everything nicely. Here you go. You really do have to ride the bikes to see what you like, though.

I know what you mean about the sticker shock. My other sport is fencing, and while it's also not a cheap sport, the most I'd ever have to spend at one go was about $100. And being a college student, a bike's a lot of money!