I will agree with the people who have recommended that you look for a used bike. I'm sure you could find something pretty good, and I trust older components from more than five years ago more than the current stuff.
But, then, buying a used bike means you probably don't get much of a warranty. It's not going to be backed by the shop quite as well, and it's hard for a novice to look at a bike (used or new) and tell what's good on it.
As for new bikes, there are only two readily-available brands I will still recommend: Specialized and Cannondale. Since price is important to you, I'd recommend the former.
Ten years ago there were tons of specialty manufacturers I could have recommended; Schwinn (my favorite), Gary Fisher, GT, Trek, to name a few. Most of them have been bought by a company called Pacific and stripped down to department-store brands. Trek bought Gary Fisher and then went to sh*t.
I will absolutely, 1000% not recommend Trek (or their other brand, Gary Fisher). I helped a friend in MI pick one out, thinking I could still trust the brand. I had to fix that bike on the trail more times than I care to talk about. Another friend wanted a bike, and I figured I'd give Trek another chance. I helped him pick a more expensive model. It was every bit as bad as the first. Both had tons of warranty repairs (as long as the warranty was good...then after that both bikes cost the owners money, of course) and both were a nightmare to keep well-adjusted.
I used to be a bike mechanic. I worked in shops during high school and college. I know how to turn a wrench. Don't buy a Trek.
Specifically, one of those bikes
was a 2002 8500, recommended earlier. What a pile.
