BabyCenter - Plain Style Cotton Crib Baby Bedding Set. Since the babies are mostly asleep during their first year, therefore they breathe in whatever emits from their bedding, mattresses or pads. You have to make sure that the bedding you purchase is made of a pure fabric. 100% cotton is best for baby bedding, especially for newborns. This way your baby will not be exposed to allergies or any other diseases. Cotton baby bedding is the best for your little precious baby.