I use sheets as backing about half the time.......the ones I use most often are Walmart brand 200 thread count. They are either cotton or a poly/cotton blend. They are stable enough to work with and soft enough to be comfortable. I usually buy a King for approximately $15 and use the excess for borders and/or binding. It works great but I always cut off all hems and selvages, square it up, before I start putting it with the quilt.
I've heard that the higher thread count, being more dense, can be a bad idea because the needle will break the fabric threads since they are so close together .....whereas on a lower thread count the needle will go between threads. Whether that is true or not, I don't know; but it makes a good story.