First...i have said before that i am not a Sunbonnet Sue fan...but that quilt with the one "odd" Sue is just too precious. I really like it.
I can only say that if it were me - and i'm not sure the size of your appliqued squares - i would use a batting that allows you to quilt up to 10" apart. That way, you could SITD around each block and in the corner blocks - not a lot of quilting, but more than tying. And i'd definitely use muslin for the backing.
Someone put a lot of work into these quilt tops....it's great that they are finally going to be finished. Good luck...don't forget to post as you finish them - i'll look forward to seeing what you decide.