There are basically three types of BCs: Jacket, back-inflate and BP/W. Jackets have an air bladder that wraps around the diver. One of the things people like about them is that they encourage an upright position in the water at the surface when they are inflated. One of the things people don't like about them is that, when you inflate them, they can squeeze your torso and be uncomfortable. They are also bulky
Back inflate BCs have all of the inflation bladder behind the diver, so nothing wraps around you. They are made as one piece and usually have a soft, padded back. They are sometimes criticized as tending to push the diver face forward on the surface, but this is usually true only if they are overinflated, or if the diver has a very large amount of weight on the front of his body. They tend to be more expensive than jackets (I don't know why).
Both jackets and back-inflate BCs can have pockets and D-rings to attach things to.
A BP/W is a modular system, consisting of three parts: An inflation bladder, a backplate (which is usually metal and not padded), and a harness. They are three separate components and may even be purchased from different companies. Bladders vary in size (lift), shape and construction. Backplates may be steel, aluminum or plastic, depending on your need for weight. Harnesses may be simple one-piece webbing, or more complex systems with releases. Generally, a BP/W setup will not have pockets unless you purchase and install them separately, so a lot of people diving them put pockets on their exposure protection.
Buoyancy-wise, the BP/W system can have the advantage of moving a significant amount of weight (five pounds or more) up onto your back, so that it's easier to maintain a horizontal position in the water. This can also be accomplished with the other types by using the trim pockets which are present in some of them.
You can read TONS of threads here on Scubaboard about the three kinds of BCs, and people's perception of their advantages and disadvantages. In the end, you should buy what is comfortable in the water and fits you well, and suits the kind of diving you are planning on doing.