Hi there,
my husband and I have 4 cats and are expecting our first child in October. From years of living with cats and being connected to a variety of cat welfare groups, I would recommend a "teenage" cat, somewhere between 6 months and a year and half.
A young kitten doesn't have the skill and coordination to interact with younger children (including to get away when your toddler wants to pull the kitten's tail) and younger kids don't understand yet that they might be playing too roughly. Scratches and injuries to both kids and kitten can result. A "teenage" cat is big enough to get away when appropriate but also very active and interested in play with strings, balls, toy mice, etc. An older cat is less interested in play and not as adaptable and exciting. As other people have mentioned, kittens are a lot more work because they get into everything and want lots of play and attention. A "teenage" cat has started to get a bit more independent but is still quite involved.
I would recommend taking your kids with you when you choose the cat. You want a cat that doesn't get scared of the children and that likes to be touched and carried around. Make sure to help your kids learn how to pick up a cat and respect that sometimes the cat won't want to play. An easygoing and friendly cat will tell the kids this by moving away, followed by mild hissing and growling, and eventually possibly a scratch if they aren't being listened to. If everybody learns to respect each other then cats can be wonderful pets for kids.
I would definitely emphasize that hands are not toys and use strings, cat "fishing poles", and so on because this avoids many scratches. Hands should be for love and petting. I would also recommend making sure that there are places the cat can get away from the kids when he or she needs a break...a high shelf or cat tree where they can watch what's going on, a closet with a cat door that is otherwise locked, or something similar that works with your home and lifestyle. This gives the cat a break when they need it and means they are much happier when they really do want to play. Good scratching posts that are treated with catnip and used as part of play can really help behavior too. We actually have one in most rooms so that there is always one for the cat to scratch.
Oh, I might also recommend making sure nobody is allergic to cats in your house. It would be horrible to find just the right cat, bring it home and have sneezing, itchy eyes, and hives be the result. Having to return the cat would be hard!
Anyway, those are my thoughts. I love cats and am always happy to share stories and advice!