I really love the way the blocks seem to just sit on one piece of gray fabric. That is a great look. I also appreciate all of the answers you received so thanks for asking your questions! Good luck with the quilting, looking forward to seeing it all done.
I prefer the look of your first plan for quilting but either way would probably work.

I think I would do a serpentine stitch down the center of the grey sashings starting with the center and go out to each side. Then I think you could do a free hand wandering stitch in each square. This should be enough stitching to hold for most styles of batting. Look on your package and see what spacing is required.It is a cute little quilt.