for borders i would do a series of skinny borders tone on tone or solid - 1 for each color in the quilt.
so cream, grey, green, navy, etc - i'd start with the lightest color and a 1/2 inch in size and then i would add 0.25 (so the next strip is 3/4 inch) to each additional border and of course working from lightest to darkest fabric
sew them all together in a strata and then attach and miter at each corner.
for the backing fabric i would go with a batik with similar colors and design (a leaf or a flower) or a flannel with a similar design.