If you'll look through the picture section most people show pics of the back as well as the front of their quilts.
For backings I have used sheets (I've had no problem, but some question the quality of the fabric), I've pieced the back from leftovers of the front, I've bought yardage and cut it in half then sewn the long sides together, I've bought actual backing fabric that's 108 inches wide so you just need to buy enough to cover the width of your quilt. There are many, many ways to do a backing.
Here's a pieced back -
http://www.quiltingboard.com/t-159308-1.htm
another one
http://www.quiltingboard.com/t-148289-1.htm
This is backing fabric -
http://www.quiltingboard.com/t-155863-1.htm
Yardage that was cut and resewn -
http://www.quiltingboard.com/t-154003-1.htm
Your larger squares would work fine. I think the pieced backs are most interesting.