I think a white would show up too strongly against the darker colors, and give a jarring affect. I think a very light blue or very light purple would look quite nice. (My goal is to pick a thread color that shows up against all colors, but at about the same level with all.)
For a quilting design, I think a design highlighting squares might work well, like this one:
(I know the usual advice is to use curving quilting when your piecing is angular visa versa, but I just feel like this might be a good exception.)
Looking at your piecing, I see a few pinwheels there, so another idea is to pick a quilting echoes that a bit. I didn't a quick search and found a few images, below. I don't love them, but maybe they will trigger an idea.
