I backed it with a piece of flannel (which I bought YEARS ago with the idea of making a nightie for myself). I did not use any batting, because I felt the corduroy was heavy enough; it didn't need the extra insulation.
I took my time quilting it using either red or light blue perle cotton #8. Sometimes I used the big stitch, but more often I reverted to a smaller stitch length, simply because that is what I am used to. I had no overall quilting plan, so each section was decided as I came to it. There are two pieces of velvet in the quilt, which I left unquilted. The binding is made from a tight velour or suede cloth, which was in the bag along with the corduroy pieces that I had received.
Friends asked me if corduroy is hard to hand quilt. Actually no. It isn't as tightly woven as one might expect. Not having a batting to needle through also helped.
This is the most free formed quilt I have ever made. The more I look at it, the more I like it!