Many chickens make great pets for kids, but I personally prefer bantams. They're smaller (which makes them easier for small hands to control), come in a wide variety of shapes and colors, and have very entertaining personalities. They also seem very intelligent, though I've never tried to train mine to do anything. As for what type of bantam, there are lots of choices.
If you want a really unique bantam, get some Silkies. They're cute, soft, and very docile. Another great breed is the bantam Wyandotte. They come in beautiful colors, are round and fluffy, and also have nice temperaments. An easy to train breed is the Modern Game, though they do have a rather unusual appearance. There are many other breeds that are good with kids, too: bantam Brahmas, Cochins, Dutch, D'Uccles, Plymouth Rocks, etc.
If you want to combine a pet with production, you could get large fowl chickens instead. Large fowl are just as easy-going as bantams; their only possible drawbacks are that they take up more space and can be a little harder to handle. Still, some good choices are Wyandottes, Cochins, Plymouth Rocks, Orpingtons, Australorps, Sex-links, Easter Eggers, and Ameraucanas. Those breeds will provide you with some delicious eggs, and are usually excellent around children.
In case you want to see photos of some of the breeds I mentioned, this is a good website (with photos) on poultry breeds:
http://feathersite.com/Poultry/BRKPoultryPage.html