For size, you will likely find them more in small, medium, large, extra large. It's just that frame design is different than a hardtail, so in inches might not be too accurate, but probably you would be looking for a medium or a large, depending on brand. A bike store should help you get the right size.
I think that your budget is nice, you won't get the top of the line, but you'll be able to find a pretty good bike.
Find which bike shops are in your area, and which brands they carry. There are several brands that could be pretty good, this brands are some I would look at in no special order:
Trek, Specialized, Cannondale, Giant, Jamis, Kona.
Talk to the shop salesman to see which bikes they suggest. One of the things you should consider is which type of riding you would like to do most. It's not that you have to come up with a perfect description or fit a specific category, but more importantly what you want to do the bike to do. Do you like to do long distances? Or more jumps? Or go to a trail and be able to get to the top to enjoy the down part? Do you want to do more adventure riding, or go to a park with bike paths? Do you want to do extreme stuff, like jumps and drops and man-made obstacles? Also use it for a bit of road riding? I think that information would help the salesguy to offer you some models.
