Regular cotton binding would work but why would you use it when the fleece is right there and can easily be flipped to the front to act as a binding. The cotton binding would just add an extra layer of fabric which you don't need and would need to be cut a wider to cover the extra thickness of the fleece. A 1/4" binding would just not work for this kind of quilt. Any quilt with a fleece backing is user friendly and your user will not be checking to see if you used a cotton binding. Using the backing as a binding is a quick and easy way to finish this type of quilt. The baby will love it.