I think using 100% cotton sheets is a practical idea in your case. They usually hold up well to many washings as they are designed to. The problem is it is difficult to find a print one that will match the front, so you are left with solids. I personally like making quilts with two pretty sides, but I might rethink that if I made a lot of charity quilts.
Buying bolts from Marshal Dry Goods is good option. As mentioned, their Dream Cotton is very nice, and even a few of their MDF Classics have a better weave than others. Lots of people have used their large size 108' quilt backs for $7.95 a yard. You can easily make a teen size with two yards ($16)