You want a hard-tail because full suspensions are junk at this price and unsuitable for most people (heavy and squishy makes riding harder).
The Trek 3700 is the type of thing worth looking at. Giant, specialized, kona, and most of the good brands have entry level models under your limit, but be prepared to spend most of it. All these brands are equal, so brand isn't worth getting hung up on. As long as you go to a real bike store and not a department store, you'll end up with a decent bike.
All bikes come in several sizes and one size will be good for you. The bike shop can help fit you, but ideally if you stand over the top bar with both feet flat on the ground, you should clear it by 2-4" to have a good fit. You might consider a bike a bit too big mind you, or you'll outgrow it by next year.
