beginner
For a beginner's bike, you'll probably be more concerned about the price than anything else. So you'll probably want an aluminum frame as opposed to carbon fiber which will more than triple the price. Moving on to cranks and sprockets, your legs probably won't be fine-tuned for biking, so you're going to want a sprocket with 180 teeth. This will allow you to pedal easier, but consequently you will not be able to go as fast. Moving on to gears, you're going to stick with a 7 or 8 gear bike, seeming how it would probably be the cheapest. Moving on to tires, you'll want the tire specified for its own terrain, meaning you want to buy a mud tire if you were to go biking in the mud as opposed to a dust tire which would go in the dust.
Intermediate
Intermediate biking is more expensive than the beginners bike because you are probably wanting to get into more specific techniques. Such as jumping. When you're jumping you need to concern yourself with bottoming out your suspension. and how you prevent this is by knowing what you want to do how high you want to jump and how far. So you'll want a full suspension mountain bike that is a rated for jumping. you should not jumper on a bike that has lousy suspension because it could bottom out and be unsafe to ride.
Expert
Expert biking. if you would consider yourself an expert bike or you probably don't need my opinion oh, but I'll give it anyways. An expert biker is somebody who probably bikes competitively. And for this you'd probably want to the most expensive high end quality bike there is.