I grew up with cats, dogs, rabbits and the occasional home for the holiday chick and as an adult I now have cats and am not fearful of any household pets. I have friends who have grown up with no pets in the house and consequently are quite fearful of animals and reluctant to be near them. The two might not be linked but I do think it is healthy to introduce children to pets from an early age. You can teach them how to act around animals, how to respect them, how to fuss them and how to not scare or hurt them. It also teaches children how to be responsible for a pet as they can help with feeding them, walking them, cleaning out cages etc.
What pet is best depends on each family individually. If there is no one home during the day then a dog probably is not the best pet but a cat would be happy in that home. If you are rescuing an animal rather than getting a puppy or kitten from a breeder then check their history to see if they are happy around children and how they behave on their own and in company.
If your house is not ready for a big pet like a cat or a dog then chose a pet that is slightly less demanding and smaller. Fish can be quite easy to look after but they do require regular tank maintenance and are not at all affectionate. Gerbils, hamsters and other similar rodent type creatures can be cute little pets but again they need fairly regular hutch/cage maintenance and some are nocturnal so will sleep all day and make a racket all night in their cages.
Cats are a fairly simple pet to look after, they normally only require two meals a day, a clean litter tray or cat flap for access to the outdoor loo and some fuss, however the bigger the animal the more expensive they seem to be. Dogs are a great pet as they are really affectionate and rewarding but they require a lot more time, effort and energy. And the bigger the dog the bigger their need for exercise and their appetite, whilst you can get food to cater for larger breeds (Royal Canin Giant, Giant Sensible and Giant Adult for example) remember they will take up a lot more space and time.