Congratulations on your decision to adopt a cat! There are several factors to consider before making the final decision between an adult or a kitten.
Do you have children under the age of six?
Although there may be exceptions, it is generally not recommended for families with very young children to adopt kittens. Little kids simply do not know how to handle kittens properly, and could inadvertently injure a kitten or be badly scratched.
By the same token, geriatric cats are impatient with youngsters, both of the human and feline species. The best cat for such a family might be a cat two to three years old, who knows how to take care of himself around youngsters, yet might be receptive to some gentle petting.
Are you senior citizens?
Kittens require a lot of care and supervision. If you've ever baby-sat with young grandchildren, you'll know what I mean. Kittens are very like human toddlers. They get into everything; they race around like mad, knocking things over; they have voracious appetites. And when bored, they become mischievous.
Depending on your own age, you might be comfortable with a cat anywhere from 10 to 15 years of age. Many of these cats come from loving homes, and are accustomed to human companionship. You could live out your golden years quite happily with such a cat.
Do you both work outside the home?
A kitten would probably be out of the question for all the reasons cited in the question immediately above.
Any adult cat should work for you, provided he or she has plenty of entertainment activities to keep busy while you are at work.
If one of you is home during the day, a kitten is an option, but be prepared for a workout. You'll have tons of fun with it, but you'll also have to worry about a "kitten-sitter" if you want to take a weekend trip.
A plug for older or special needs cats
If one of you is home during the day, I'd love it if you would consider adopting a senior cat or another cat with special needs. These cats are often considered "unadoptable," and are almost always overlooked in favor of the cute kittens who crowd the shelters. In "kill" shelters, they are almost always the first to go. They can be lovely, loyal pets, who will reward you with unconditional love.