I use fleece as my batting/backing - especially for my many donation quilts. I would precaution that fleece does have a slight stretch along the width. For this reason I do a heavy quilting (usually along my pieced seams) in all directions just to help stabilize the stretch. I use a 1/2" binding to also contain the shape.
All and any 'fuzzy' polyester fabrics should be washed in cold water and dried on air-dry or just hang to dry. The addition of fabric softeners in the wash cycle or in the dryer will cause the 'fuzzy' fibers to stick together and the cuddle/softness of the fabric will be lost.