Hey Crabby, I could not find the pattern you are asking about, but I would use 1/2" to 3/4" hardwood such as walnut or mahogany. You could also use Baltic birch plywood that you could stain or paint.
OK, I found the pattern. I would not go thinner than 1/4", but I probably would use 1/2" hardwood. I like mahogany, so that's what I would use.