Before Hancock's closed, I bought Cotton Sheeting fabric by the roll for all my quilts. I love the closer weave and no seams on the back of the quilt. I do all my own long arm quilting so the close weave is not a problem.
The one thing I wouldn't do is use an older sheet for the backing. Sheets do wear out and start to tear or rip as they age. It takes a new one a long time to do that on the back of a quilt, since quilts are not washed very often.