What I'd recommend is a decent hardtail mountain bike in the sub-$1,000 range (though you should plan to use the rig after your trip, too, if you are going to put in that kind of money). A grand or less will get you a good frame, reliable components, a quality front shock absorber, and the ability to upgrade or replace any component as you go along.
And really, the choices are many, many, many. Marin's Nail Trail ($840; www.marinbikes.com) is a representative examplealuminum frame, Answer Axel fork, a mix of low- and high-end Shimano components (XT where it matters, Deore where it really doesn't). Shockingly, it also features hydraulic disc brakessomething found only on $2,000-plus bikes not that long ago. Or, take a gander at Giant's XTC 2 (usually $1,100my guess is you can find a sale; www.giant-bicycle.com) offers a really great mix of components in a light, affordable bike. A great buy, with a Rock Shock Duke fork, Shimano components, even Time ATAC pedals. K2's Zed 2.0, meanwhile, offers solid performance for around $500 (www.k2bike.com) .
Of course, you'll need some extras: Helmet, if you don't have one (Bell Influx II is a good choice for $60; www.bellbikehelmets.com), and shoes (Cannondale MC610, $80; www.cannondale.com). Also gloves, shorts, jersey, pump, and the like, but that's more a matter of taste and any bike store can outfit you with what you need. I do recommend giving some thought to eyewearclear or yellow lenses work best for mountain biking because they offer good visibility when moving through a forested area or in and out of shade and sun. Try the Smith Buzzsaws, for $90 (www.smith-optics.com).
Keep the rubber side down, and have fun!
For this year's best mountain bikes, check out Outside's 2004 Buyer's Guide.