For quilting down, if your machine has an option chose something like a serpentine stitch, that is something a bit wider and looser than a zig zag, but go ahead and run that down 1/2" so wide right over those major seams to hold them down.
Depending then on how big your sub-units are and what your batting wants, further grid it down using that serpentine stitch. It is an easy utility stitch that makes things look fancier than they are and has the added benefit of basically appliqueing the top through the layers.