I am a big fan of Specialized. I've heard that some people don't like them because they are a big corporation ("the man"), but that seems silly to me... they make awesome bikes in my experience, and the more successful a company is the more money they have available to spend on engineering even better bikes. A few other brands that you'll find out there that make mountain bikes include Trek, Jamis, Cannondale, Giant, and Kona. After you get above a certain price range they all make good bikes, they just differ a bit in what the specific components on the bikes are.
I'm a fan of Hardtail bikes for a few reasons. First of all they have much higher pedalling efficiency.. you'll spend more energy pedalling a full suspension bike because some of the power you put into the pedals goes into compressing the rear suspension instead of driving the crank (although there are 'smart' suspensions which work to reduce this effect). Second they are way cheaper-you can get an awesome hardtail for $1000 but only a midrange/low-end suspension bike. Finally they require less maintenance. They also weigh a bit less.
It has to get pretty rough before I start wishing I had a suspension bike. They are obviously very cool and they are a lot of fun but for most of the trails I've been on a hardtail has been plenty, including most 'expert/advanced' cross country trails.
The biggest thing I wish that my Hardrock had was disc brakes, but I don't think you can go wrong with it as a first bike. Decent disc brakes are definitely an option for under $1000... I don't know much about how the different ones differ but I have heard to go with hydraulic brakes over mechanical.
Keeping your budget in mind though I'd recommend something like this:
http://www.specialized.com/us/en/bc/SBC ... e=Mountain
There used to be more higher-end Hardrock variants, but now it seems like they don't have as many and I think that the Rockhopper is a better buy now (I also only spent $500 on my bike and your budget is twice that). There's also a 29" version of the Rockhopper. The only difference with the more expensive Rockhoppers is that they have 'higher-end' components, which doesn't really matter for most things because they're just lighter versions of the same thing.
I don't know much about other brands because I'm so happy with my bike, haha, someone else will have to talk about that...