I think I would either paint it or let it be -- i don't really see a gain to putting a color or pattern at the backs of the sections, and it will make decorating the shelves a lot more complex. As a test, cut up some wrapping paper and tape the squares into a few sections to see how it feels -- try a few solid and a few patterned, and I'll bet at the end of the exercise you have a bit of a headache.

I'd paint it the same white as the kitchen cabinets and do either a blue/white to play off the rug, a kelly green or the poppy

or even a gold

Or, paint the whole thing a rich, deep Indigo

Paint it the same white as the kitchen cabinets. Accents can provide color or texture with metals or glass.

Erin J could you please clarify - are you painting the entire cabinet or just the back walls of it?

Cut pieces of foam core to fit the backs. Either paint the foam core, or paper it ( scrap book papers are very nice). Then just push the foam core into place. You generally do not need to affix it....it just stays in place