I would use a tone-on-tone dark fabric for the background, matching any of the darkest colors in your layer cake fabrics. (Dark fabrics make other colors stand out.)
Then I'd do a double border, the innermost being very light in color (tone-on-tone, probably cream) and very thin (1/4" - 1/2" finished). (Actually, because this border will be so thin, you can use a solid color instead of tone-on-tone.)
The second border would be relatively wide and made from a tone-on-tone fabric of your (or your mother's) favorite medium color that appears in the layer cake fabrics. For example, you might choose either a red or a turquoise or a tan. All would be beautiful.
For binding, you could repeat any of these colors.
Hope this helps! (Wish I could go fabric shopping with you. It's my favorite part of quilting!)