I would just make sure to pre-wash all fabrics to ensure all possible shrinkage has taken place, especially with the difference in fabrics. Fleece has a reputation for shrinking quite a bit. So does cotton, but not as much.
I like spray basting. Minimizes/eliminates puckering.
I'm fond of using the Topstitch needle, even in my quilting. Nice and sharp. Since you don't have to worry about stretching with the cotton, don't worry about it with the fleece. You only have to use stretch stitching when you're sewing a stretchy fabric to a stretchy fabric.
I agree with keeping the quilting simple. SITD, grid lines, etc. with a walking foot. That's what I'd do.
Sounds like you have a winner of a project there! Don't worry about it. I've mixed fabrics plenty of times without problems.