Composters can range from the nonexistent to the expensive, top of the line rotating, multi-chamber ones.
By nonexistent we mean that you can assign a portion of your garden in which to do your composting or dig a pit for the purpose and not need any kind of composter.
However because the rubbish that transforms into plant compost is not very seemly and not pleasant smelling either, most people do prefer to have a composter or a compost bin.
Your budget would have to be the single most important deciding factor for selecting the composter. It is important to remember that composting is a natural process which will take place regardless of whether you stick it in a hole in the ground or use the best money can buy.
A multi chamber, rotating composter will speed up the process of composting to begin with; however this may become immaterial in the long run, once you have the process of composting going. However you have to be aware that a static composter is the easiest to maintain and perhaps the most long lasting.
An important factor is the size of the composter. This is determined by the amount of waste that your household produces or is readably expected to generate on a regular basis.
It actually makes more sense to have more than one smaller bin, so that when one is full, it can be left for the composting to be complete.