You can use cotton on the back, just prewash to shrink the fabric. Depending on what the quilt looks like i would opt for just doing a stipple on it . It sounds like a scrappy quilt.
Start practicing some free motion stippling on 15 or 18" sandwiches. This is the easiest motif to learn. You will be doing alot for your friend and learning a new technique for yourself. :thumbup:
The idea of showing her what you did with the quilt is wonderful and then you can offer it back to her as a gift of friendship.