If I have a very busy or bright top, then I look for a subdued backing. I have pieced backings and like the look, too. In January, I go to Sears and JCPenney to see if they have any flannel sheet sets on sale. If I like one or two, I buy them at very discounted prices. There's a lot of flannel in twin, full or queen size sheets. I will also use 100% cotton sheets, 180 thread count or a poly/cotton blend as long as there is more cotton then poly.
There are times when I just see a fabric and know it will work for the backing! That's usually a more expensive way to pick backing, though.
All methods work, though!