I've used both sheets and muslin for backing. I've found "utility" muslin is a bit heavier and washes up beautifully. I do remove all of my fabrics promptly from the washer and take them straight to the ironing board.
If sheet shopping, don't hesitate getting a "set" you can always use the fitted sheet on the next smaller (i.e. queen fitted sheet for a full quilt back) size for a second quilt back. I like to get mine from Bed Bath and Beyond, and I "feel" them first to make sure they feel nice.
Just be careful I've seen extra wide muslin $$$ more than quilt backs.