Sandi, busy doesn't have to mean dark colors or even many colors. A light colored tone-on-tone or something with a muted design would work well on the back of the BOMs if you are worried about shadowing. Any solid fabric will show the quilting stitches more, whether they are done by machine or by hand.
However, this is the fabric that I used on the back of mine, and nothing shadows through. I used a Hobb's Heirloom (80/20) cotton batting.
(I used the background fabric as a "focus fabric" to help me choose the 50+ fabrics that I used in the quilt. These are the ones I started with, but I added about that many more.)