Mountain bikes (or rather POSs that look like mountain bikes) are the "default" bikes these days, so I can see why you're looking at those. But AllenG has a very good point: if the trails you're doing aren't going to be very technical, and if you will be riding a lot on pavement, you might want to look at cyclocross bikes. They are used for racing offroad. They're like road bikes (fast, aero) but are tougher and are able to take wider tires etc. if necessary. However, I'm not quite sure what you mean by "mountains". If you mean paved trails/roads in the mountains, the cyclocross recommendation holds. But if we're talking about rocky trails or just rocks with hardly any trails at all, then an MTB is definitely the thing to buy. Which one - I don't know (not an mtb expert here, and are not familiar with the terrain you'll be riding on and the type of riding you'll be doing).

There is no reason to be stuck on Trek. There are lots of good manufacturers around. In fact, you should probably shop for a bike shop as much as for a manufacturer. Find one with knowledgeable mechanics, friendly service and a good free tune-up package thrown in with the purchase of the bike. Bikes need maintenance, and a good relationship with your LBS (local bike shop) helps. Once you decided on the style of the bike and found some good shops, test-ride the bikes they carry in your price range and buy the one that feels and looks best.