Mountain bikes get even more specialised than road vs. tri bikes, it all depends on what you intend to do with it. XC racing, light trail use, freeride / downhill, all of these demand different things from the bike and so there are different bikes that work best. Not that you can't DH on a hardtail, but I wouldn't want to.
In general, a hardtail is less maintenance than a full suspension, an XC oriented full suspension will be faster and more comfortable over most terrain. A lot depends on your local trail conditions as well as to what is best.
Decent mountain bikes start at well under $1000, and go up from there to whatever you want to pay.
There are a load of good manufacturers out there. Have a look at the Trek / Gary Fisher / Klein, as well as Specialised, Giant, Cannondale. All make decent bikes at good prices. There are a load of companies that specialise in mountain bikes that you shouldn't overlook, like Rocky Mountain, Santa Cruz, Brodie, etc. etc. There aren't too many truly 'bad' bikes out there anymore.
Swimming Workout of the Day: Favourite Swim Sets: 2020 National Masters Champion - M50-54 - 50m Butterfly