At the thrift store, the high quality bedskirts often come with high quality tops also, and it is usually white fabric that can be used in your quilts.
The other types of tops are great for foundation piecing.
I love to use the poly tops that have the little holes in them as backing for the squares I cut from t-shirts when I do t-shirt quilts. I really don't like using fusible web stuff. The knit sews great to the poly and it is light and so easy to work with. It stabilizes the knit very well in my experience.