I think soft cotton poly fabrics, and flannels work well for the quilt backing. It is the fabric that will be up against your skin.
As far as the outside...you can use anything that works. I am working on a "multi-media" quilt with knitted squares, corduroy, etc.
Look at crazy quilts. They have velvet, ribbons, and lace.
Never throw away fabric. If you need room, though (having watched one too many epiosides of the tv show "hoarders") ...make ebay your best friend!
Nikki