The cutest animal at the shelter could also be the one most likely to fray your nerves — not to mention your rug. “We steer folks away from a choice based on appearance and toward a deeper compatibility,” says ASPCA vice president Gail Buchwald, who adds that since most shelter professionals keep information on their animals’ medical and behavioral histories, they’re crucial to helping you find a good match. Dogs five years or older are good for homes with toddlers, who can be toppled by rambunctious puppies, and for people who work outside the home, because of more mature (i.e., tougher) bladders. If cats are your fancy, young families should also think about a mature animal: Kittens have fragile bones that can be broken by eager little hands. Betsy Saul, founder of Petfinder.com, a database of 9,000 animal-adoption groups with offices in Pittstown, New Jersey, and Tucson, suggests that people consider less conventional pets, like birds, fish, and guinea pigs: “They need homes and love, too.”