The first thing to do before purchasing a bicycle for any reason is to know what your primary riding is going to be. Most people initially purchase a dual use bike, something that can be ridden on road and off road. Eventually, when the bug bites big it'll be time to invest in a bike that is all muscle for the mountains.
One of the ways that mountain bikes differ from other bikes is that they have very strong, lightweight frames, multiple gears, powerful breaks and wide tires. A comfort bike, or recreational weekend bike, touring bikes and cruiser bikes are built more for comfort than durability. WIthin the mountain bike category there are several types of bikes available; the cross country bike, the trials bike, the downhill bike and the jump/slalom bike.
Generally the largest percentage of mountain bikes sold are in the cross country, or XC classification. These are good dual purpose bikes. They are lightweight and good for riding over tough terrain, but they are also comfortable for road riding.
Jump/slalom bikes are also good dual purpose bikes. They are very strong and have an excellent front suspension.
Downhill and trial bikes are for serious mountain bikers. The downhill bikes have both front and rear suspension, disc breaks and are very strong. A trial bike is for a very skilled rider. Trail riding itself is a very competitive sport demanding a lot of precision. Most riders of downhill and trail bikes build their bikes from scratch, choosing each component individually.
You will want to do a lot of reading about different types of bikes, and you'll want to visit many bike shops. A cross country mountain bike can cost between $600 and $800 or more. Some bikers say that your first bike should be the best bike you can possibly afford, even if you think that it's too much bike for you. If you buy a low-end bike initially and then find you want to change components later it can get costly. Before choosing a bike you will want to ride it. Most dealers allow for a 15 to 20 minute test ride. If you do a test ride make sure you go "off road" if you can, even if it's over curbs and grass. You want to get a feel for the bike.