How to quilt it really has to depend on your skill level and what you're able to do with your machine.
I think those solid fabrics and your very graphic design call out for some spectacular free motion quilting -- if you're not familiar with Angela Waters' books, blog and beautiful modern quilting work, check them out and see if something like that would inspire you. She tends to match thread to each fabric and let the texture of the quilting be the star. Definitely labor intensive with a design such as yours, but the results are lovely.