If it's a wallhanging, anything goes.
But if it's going to be laundered regulary I'd use dupioni silk for the backing as well.

Regular quilt shop quality cotton would be fine.

As for batting, may I ask is this a wall or bed quilt? Are you looking to do lots of detail quilting and have lots of definition? How this quilt will be used and quilted will determine what is the best batting to use.

I am making a quilt using Silk dupioni fat quarters and have no idea what to use for batting or backing. Any suggestions?