I'm a mom of two (and soon three) and do only quilt for babies or children.
After trying many different kinds of batting, I must say that if you don't mind being a bit more expensive and if there is no allergy known to wool, this is the best choice. More "fluffy" than 100% cotton, cool in summer and warm in winter, natural, stay soft and souple, etc. I made one for my daughter with wool when she was 3 years and 2 years + 50 wash later, it is still looking like new and so soft and cuddly.
Bamboo is more souple from the start and have more drape, but it doesn't get any softer with time.
Cotton/poly is a good alternative to wool; it`s cheaper and the result is quite the same.
I made only one from polyester (my first, following the suggestion of a LQS woman). Didn't like it at all. And as a mother, it`s true, you don't really like the idea of your kids sleeping under polyester every night.