Sounds like you've got it all figured out already, really. The shirts sewn in rows with a plain seam is just fine. The shirts are not going to unravel, so no seam finish is required. I would personally iron the seam open as that's what I prefer. I think it makes the seams less bulky. Then, for the back, go right ahead and use up those different pieces. I think it makes a more interesting quilt to have a pieced back. I've done that lots of times, whether by necessity because I didn't have enough of one fabric or by choice to get more fabrics and colors in. It always looks great.
Good luck, and be sure to post a photo of your finished quilt. We'd all like to see it.