Well, that is just amazing for your first quilt!
I have an antique irish chain done by my grandmother eons ago, and she treated the chains much as feline fanatic suggests -- with straight diagonal lines through the chains -- then she did some fancy stuff in the plain squares.
For the plain strips next to the Seminole strips (bravo on those strips, by the way!) you could mark and stitch diagonal lines in two directions, which would make diamond shapes where they cross over. I've done this on a domestic sewing machine, and it is not too difficult to change direction like that.
Do you have a walking foot? If not, you should get one -- you'll get lots better results. And baste well -- it is unbelievable how lumpy a quilt can get that is not basted well, when you try to machine quilt it. I really like the spray basting stuff. It is easy to overspray, so I have gone to spraying the interior of the quilt, then pinning or hand basting the borders and outer edges.
Hope this helps!