If you're a typical beginning rider, you'll probably be happiest with a "trail," "all-mountain" or "cross-country" full-suspension mountain bike. ("Cross Country" is a lighter bike that's designed for speed and efficient pedaling, best for smoother dirt trails and long rides. An "All Mountain" bike is more solid with a suspension designed to take bigger hits -- so it's a bit heavier and might pedal uphill less easily -- and would be best for a rider who regularly rides rough rock and rooty trails.)

Rocky Mountain Instinct, a lighter cross-country bike often used for racing.

First determine what type of bike matches the type of riding you want to do. (Smooth dirt trails only, or will you be bashing rough rock in Moab regularly?) A good-quality cross-country bike is usually a bit less expensive than the same quality in an all-mountain bike.

Now look for a light frame made by a respected manufacturer in a size that matches your body: S, M, L, or XL. Carbon frames are very light, very expensive, and handle vibration and little bumps better. But not all aluminum frames are created equal. The type of alloy and the construction technique makes the difference between a horrifically heavy bike and one that's almost as light as a carbon frame. The lighter the bike, the more you should expect to pay.

Rocky Mountain Slayer, considered a trail or all-mountain bike. Note different suspension for increased "travel," with beefier components.

Next look for quality components (brakes, shifters, etc). If you buy a bike with low-end off-brand components, you'll be constantly fixing and adjusting. Look for at least middle-of-the-road brakes and shifters made by a major manufacturer such as Shimano or Sram.

If you know what you're doing (or have expert help) you can find a good bargain in a used bike. If you're not confident about picking out a good used bike, it may be worth the money to have your local bike shop sell you a good solid entry-level mountain bike.

Shimano XT rear derailleur. Look for better-than-middle-quality from respected brands.

The type of bike...
Never ask "What bike should I buy?" or "What's the best bike?" There are no simple answers to those questions. "Mountain Bikes" come in many types ranging from gravel bikes (which look like road bikes but with big tires) to fat bikes (which have huge tires to ride on snow). Even among "standard" mountain bikes, there are many permutations of frame type, wheel size, and components to make the bike more specific to a particular type of riding. For example, a "downhill bike" is plush and smooth on rough descents, but miserable for a new rider to pedal uphill.

Then within each category of bike, for example the "cross-country" category, there are differences that affect how much you will enjoy riding that bike. A "hardtail" mountain bike is considered a "cross-country bike." It's light and responsive -- so it's often selected by mountain bike racers -- but it's a rough ride on rocky trails. In bikes with full suspension, the suspension design affects how well the bike absorbs bumps and how efficiently it pedals. Even in same overall model of bike, the choice of frame material affects the weight of the bike, and therefore how hard it is to pedal uphill. In general, the lighter the bike, the more it's going to cost you.

Once you identify what type of frame and suspension design works best for the type of riding you want to do, it's time to consider components. Components are the shifters, brakes and stuff. The quality here can vary wildly. There are department-store bikes with crappy components that may not survive even a single rough bike ride without requiring service.

New versus used...
Bicycle components get better every year. A new bike will have the latest stuff. Yes, you'll pay more. But the bike shop will help you get the right bike for your riding style, and make sure it fits you.

If you want to save some bucks, buy a newer used bike. In general a one-year old bike in good condition should sell for less than 1/2 of the new-bike price. Evaluate the components carefully. If you have no idea what you're looking at, get help from an expert rider. Go for famous-brand components -- so you know what you're getting. Get the full names of each piece (for example, "Shimano XTR rear derailleur") and go to the company website to see where it falls within the spectrum of cheap to best quality. In general, one step down from the "best" is still very very good and it's a lot cheaper.

Frame composition...
Most frames are either aluminum or carbon-fiber. Carbon is considered high-end. These frames are expensive. They're very light, sometimes several pounds lighter than aluminum frames. They absorb little bumps and vibrations well, yet resist flexing.

Aluminum frames vary widely in quality and in weight. The more expensive aluminum frames use special alloys and fancy construction to give a lighter frame with good strength. On the bottom end, cheap department-store aluminum frames are heavy yet more brittle and/or bendable.

Pedals... New bikes are delivered to the bike store without pedals. You pick the type of pedal you want. "Flats" are the basic bike pedals we rode on as kids. Trick riders love them, and you can get some pretty pricey flats that hold your shoes well. "Clipless pedals" are pedals that lock onto special cleats on bike shoes. Cross-country riders will often switch to clipless pedals, because they increase the efficiency of pedaling. More speed for your effort, an assurance that your foot won't bounce off the pedal at a critical time, and the option of delivering power to the pedal on the upstroke.  Sample of clipless pedal and cleats, with shoe designed to for clipless.

There are several different designs of clipless pedals, meaning the cleat on your shoe must match the brand of receiver on the pedal. If you're buying a used bike, there's a good chance you'll be buying some new pedals. (If you're a clipless rider, you could simply swap out the cleat on your bike shoes.)