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Wood might cause trouble if it has excessively visible grain, driving up costs for paint and effort required. Cloth or felt stretched across the surfaces is probably a better alternative since they, too, avoid specular highlights and cover up whatever base material you choose. A thick enough bit of cloth could even be stretched across a frame without any backing. The light box in your picture would make a good starting point if you clad it in self-adhesive green felt especially since they allow diffused lighting from the remaining sides. Snap-open light boxes should be avoided since they'll wrinkle and tear any added material in no time, but any model with a tent-like set up would be suitable. If portability is not an issue and you're looking for a more permanent set up, you could even look as far as a cheap grow tent; you'd be far from the first to "abuse" one as a photography stage. They do have a serious downside in that they are light proof so lighting them up evenly is difficult to do out of shot, something you should keep in mind whichever way you go.
Building a wooden frame doesn't require much skill or practice and only a few tools: saw, set square, metal angles, screws and a suitable driver (ideally an electric drill) but does require careful attention to detail unless you want a wonky result. If you lack these tools, then make sure you do some careful cost calculations to see whether going full-on DIY actually works out cheaper.