If you Google "zipper quilt" and then click on "images", you will find photos of zipper quilts with varied quilting. There are also good photos of zipper quilt quilting on pinterest.com .
From my brief perusal of photos online, I think these quilts look best with relatively thin batting such as Quilter's Dream cotton. I was least impressed with those that had puffy batting; it just doesn't seem to go along with the geometry of the pattern, especially when quilted in curving lines.
I would definitely use a thin thread such as Bottom Line for this quilt, and I'd probably opt for black thread on the black background fabric and silver thread for the colored.
I'd probably start out by sewing in-the-ditch (not 1/4" away) around the rows of teeth to separate the background areas from the colored areas, then consider what I wanted to do after that. I'm thinking black thread lines 1/4" apart throughout the black background, then perhaps silver thread in overlapping geometric boxes inside the colored teeth. Angela Walters shows how to do easy geometric quilting in one of her Craftsy classes or videos (and in at least one of her books). Or, I also think a fairly dense overall meander would look good too; I would just do that inside the SID lines to keep the thread colors separate.
Edit: Here is a website that shows the Angela Walters boxes (example in red):
http://www.sewmamasew.com/2015/05/ho...traight-lines/