Go to your local shelter and spend some time with the cats there. There will be ones who tolerate young children and ones who don't. The shelter personnel will likely have evaluated the cats they have for adoption for different characteristics. And shelter pets know they've been rescued and seem to love their owners even more. As a practical matter, I'd probably avoid long-haired cats. They wouldn't appreciate having sticky fingers petting them. Not that short-haired ones would either, but they'd be easier to clean with a damp cloth. (Most cats really do hate baths. Don't go there if you don't have to.)
I don't think there is really a bad cat for a family, but as a tip, stay away from the Persians and those big fluffy white/tan/brown/black ones, that said, Ive had a calico cat for a long time, ans its been great.