I think it's personal preference. If I'm making a quilt for display I usually use a whole piece of coordinating cloth for backing. If I'm making a quilt to be used I go right ahead and scrap piece it all together.
As far as what to choose for a scrappy backing, there are no rules. Sometimes I find what bigger chunks I have in my stash and piece them together in a way that pleases me. I have been known to buy a yard of flannel for a backing and then cotton borders of different fabrics until the piece fits the top of my quilt. I read years ago on Bonnie Hunter's website (from Quiltville.com) that she cuts fabric into 6" squares and keeps it on hand to piece into backings. A lady in my quilt guild actually goes all out and pieces as intricate backings as she does tops.
Another idea could be to use your leftover blocks from your top, or orphan blocks you have around the house pieced with fabric scraps for a backing.