What bike should I get?

If you are a beginning off-road rider, you should be looking at a bike with front suspension only (called a hardtail), or even a rigid bike (with no susension fork). A good quality full suspension bike is too expensive to be a beginner bike. If you want the bike mainly for riding on paved surfaces a rigid bike is a better bet.

The frame

The frame is the heart of a mountain bike, and you want to make sure you get a good one. If the bike comes with mediocre parts on it you can replace them, but once you replace the frame it's a different bike.
When looking for a not-too-expensive mountain bike, remember that boring is good. If the bike is too fancy and radical looking, especially if it's inexpensive, it's probably not a good bike. Unless you're going for a full-suspension bike, the traditional diamond frame is the best (as in the Rockhopper below). Any frame design other than this will be more heavy or weaker. The only exceptions in this price range are bikes made by Haro or GT, and these bikes only have small variations on the diamond frame.

If you're not sure exactly what a diamond frame is, let's look at a bike that doesn't have one, the Specialized Enduro below. This bike has rear suspension (the cylindrical bit where the seatstays meet the frame is the rear shock) thus it requires a different geometry to accommodate the shock and the movement of the back part of the bike. You will often see somewhat odd-looking frame designs in full-suspension bikes, but they are rarely useful in hardtails or rigid bikes. (Don't drool too much over this bike. It is unfortunately well out of the price range of this article.)
Many mountain bikes today have a sloping top tube (clearly seen in the Rockhopper). This is a good thing, as it gives you more crotch clearance for the same size of bike. Crotch clearance is the distance between the top tube and your crotch when you are standing over the bike in your bike shoes. It is important because you often crash when riding off-road, and it's good to have a bike that stays out of your way when you come off unexpectedly.

To bounce or not to bounce

Since real rear suspension (as of the Specialized Enduro above) is out of the price range of this article, we'll only consider two kinds of suspension: a suspension fork, and a suspension seat post. First I'll discuss the fork.

Should you get bike with a suspension fork? I think the answer is pretty short and simple: if your main use of the bike is for riding on rough off-road, then get a suspension fork, unless your budget is really low. A good suspension fork is a real boon to off-road riding. Not only does it make the ride more comfortable, but it can greatly improve your control over the bike. For example, if you're coming down a hill and there's a small branch diagonally across the path, the suspension fork can help you get over it safely, while with a rigid fork, your front wheel has more of a tendency to by shunted aside by the branch, leaving you in a heap on the trail. Since most mountain bikes come with suspension forks, this is the easy option.

However, if you have very little money (say you want to spend less than 300 quid, including everything you'll need, like lock and lights), a rigid bike is best, even for riding off-road. For example, a Specialized HardRock Rigid is better suited to off-road riding than most bikes for that price, even ones with a suspension fork. The reason is that most suspension forks on bikes that cheap are really not very good, and while they add a bit of comfort for your off-road riding, they lack the rigidity and damping that allows you to maintain the best control over your bike through the rough stuff. In addition, the frame and other components will be of lower quality to allow for the cost of the suspension fork, and they may not be up to real off-roading. If your budget really is that low, getting a HardRock Rigid would get you riding off-road on a good bike straight off, and then when you've saved up more money you can add a nice suspension fork.

However, many people buy mountain bikes for general purpose riding, not for hard-core off-road riding. MTBs are durable, adaptable machines that can be used for a wide variety of purposes, including riding to work, touring, and just getting out into the countryside for a pleasant spin on a sunny day. If your main use of the bike is not off-road riding, you would be better off getting a rigid (not suspension) fork. Even if your planned use of the bike includes a bit of off-road riding, such as riding on fairly smooth unpaved surfaced (cinder-surfaced bike trails, forest roads), a rigid bike would be best. This is because suspension forks are more expensive, heavier, more likely to go wrong, and more attractive to thieves than rigid forks. In addition, if you stand up to pedal you can lose a fair bit of your energy in bobbing the fork up and down. On rough trails, the suspension fork is so effective at smoothing out the trail bumps that it offsets all these drawbacks, but roads are smooth enough that the fatter tires you get on a MTB provides enough cusioning for all-day comfort in the saddle. This is true even if you get fairly thin (1.5"), smooth, street-specific tires.
Decent-quality rigid MTBs can be hard to find. Many people seem to feel that suspension must be better than no suspension, even for road riding, and so avoid MTBs with rigid forks. However, good bikes are out there (some manufacturers call them "Urban bikes"), and I urge you to make the effort to find them. At time of writing, Marin make the Muirwoods, Specialized do the HardRock Rigid, and Ridgeback do a series of bikes called "Switch". These are super choices for general purpose riding.
A suspension seatpost is another form of suspension that sometimes crops up on some bikes of this price range. They usually come on bikes meant for town use, or on "comfort bikes" meant for slow riding on flat roads, rather than on bikes aimed at real off-road riding. I feel that a suspension seatport is of use either on or off-road. If you hit a pothole on the road, the main place you feel it is in your backside, and a suspension seatpost can help smooth it out. Off-road, it can help smooth out minor trail bumps, allowing you to stay in the saddle for more situations, which can reduce fatigue. It will be of little help on big bumps, which is why proper rear suspension is useful on a bike used for rough off-road. There are some drawbacks to suspension seatposts, and they are the same as for suspension forks: suspension seatposts are more expensive, heavier, and more likely to go wrong that ordinary ones. However, they are much simpler than suspension forks, and they have much less travel, so the difference in price and reliability isn't so great as with suspension forks.

Do you need disk brakes?

 

Disk brakes are popping up on more and more bikes nowdays, and a few bikes in the price range considered by this article have them. Generally, they are included only on bikes meant for real off-road riding. The main advantages of disk brakes are that they work much better in the wet (especially off-road, since mud can interfere with your braking even more than plain water) and that your rims don't wear down as a result of brake pads rubbing them, so they last alot longer. The rim wear issue ends up being the deciding factor for some people: if you ride in areas with gritty soil, you can wear through rims quite quickly. The disadvantages are that they weigh and cost alot more than rim brakes, add appeal for thieves, and make getting your wheels off the bike a bit more difficult. If you're planning to use your bike mainly for road riding, don't even consider them. They are of most use off-road if you often ride when it's wet, so you'll take full advantage of the reduced rim wear and better wet-weather performance. I would suggest that a beginner would probably be better off without them, because not having them will mean that your bike can have a better frame and components for the same amount of money. You won't really know if you need them until you've been riding awhile and know what sorts of situations you'll be riding in. However, it can pay to buy a bike that's disk-brake ready: it should have disk mounts on the frame, and preferably disk-ready hubs. Then if you want to upgrade to disk brakes it's a fairly painless process, and not all that expensive, as you'll only pay for the disk brakes themselves.