Most people who go to the shelter to get a new pet look for a kitten or puppy. They're very cute and appealing, and there is something to be said for raising one up in the way you want it to behave, rather than risk taking on a fully-grown animal that may have some bad habits. This is understandable, but not necessarily reasonable.
Older pets can make more stable housemates.
Older cats, especially, will adapt well to a single human dwelling. They are less likely to get into mischief since they sleep on average about 20 hours a day. The likelihood you come home to find your prized African violets smashed on the kitchen floor is remote. Older cats are really the best way to go if you don't have any other animals. Cats can live as long as twenty or more years if they are well-cared for, so choosing a four year old adult still gives you many years to be together.