There are two basic styles of amplifiers, as shown below. A combo amp (combined amplifier and speaker) is usually best for beginners as it is smaller and easier to carry around. The other type is a stack, which consists of an amplifier "head" and a separate speaker box containing up to four speakers. Stacks are mostly used by bands playing in large venues.
There are also two different types of sound generation systems in amplifiers. One is the valve or vacuum tube amplifier, and the other is the solid state or transistor amplifier. Valve amplifiers have traditionally been the most popular because of their ability to produce a clear crisp sound without losing warmth or depth of tone and for their ability to provide fine grades of overdriven sounds. Small valve amps also produce great natural distortion sounds when turned right up. This is more difficult to achieve with larger amplifiers, mainly because by the time you turn the amp up enough to get the desired tone it’s just too loud! In recent years there have been many advances in amplifier design and manufacture and there are now a variety of both valve and solid state amplifiers which produce great sounds. If you haven’t been playing for long, it is probably best to go for a fairly versatile one which is capable of producing a variety of sounds suitable for several styles of music. As with guitars, try out several amps before deciding.