My mother, grandmother and great grandmothers all use(d) sheets for backing. I have only done 5 quilts, but have used sheets on 3 and fleece on two...but I hand quilt using a lap frame. We try to use 300tct to 400tct, Mom says anything higher is TUFF on the fingers. 300tct does not pill, feels nice on the skin and launders really well.
Walmart has great economy priced sheets in great colors and some have come from the thrift shops...lots of Martha Stewart flat sheets and Better Homes and Gardens.