Are you using the Axiom stands or something else? I would just use cabinet grade Plywood of your choice and either stain it to match furniture, trim, or the stands. MDF could be used if you want to paint them. So far as stability goes as long as it is wider than it is high then it will be vary stable and the weight of the wood should be more than enough to keep from getting bumped over, especially if 3/4" is used. I would be more concerned about possibly mounting the stand to the box so the stand couldn't be knocked over unless the box is pushed over as well.
