I like using fleece as a back for quilts that I want to have a softer back i.e. the elderly, or babies which have more tender skin or if I want a lighter weight quilt. I don't use batting with fleece but I do when I use soft flannel for a backing.
As far as being faster I find using the pillowcase method to be faster. This method is done by putting right sides together,sewing around all edges but leaving a 3-4" opening in a seam to turn right side out. Trim corners and turn right side out. Press edges and hand stitch opening closed. Then quilt or tie the two layers together using whatever method you choose.
I hope this helps.
Sis