[cabinetman]

I would use either Poplar, Birch, or Maple plywood and use trim to cover the edges.

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[cabinetman]

How thick? It's not gonna hold a bunch of weight...was thinking 1/4 if I could get away with it

It would depend on the size, and the loads. I would use a minimum of ½" or ¾", in order to get some rigidity and the ability to use common joinery methods.

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[cabinetman]

Ok...would you cut small dados in the sides for the shelves and screw in from the outside?

Doing that you could just glue and clamp.

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