If I may, I'd like to add that 1/8th inch thick Lauan plywood is not only cheap, it's easy to find. Most home centers sell 8' X 4' sheets of the stuff, but if you can't find them, ask for an interior hollow-core door skin. They're 7' X 3' and run about $10. Interior hollow-core doors have been faced with Lauan since the '50s, so the skins to repair them are pretty easy to find.
This stuff also works great for making paterns & templates. At the cabinet shop, if we needed to make several complex pieces exactly the same, we made a template out of 1/8th inch Lauan, then used double sided tape to attach it to the wood we wanted to cut out. A quick trip through the router table with a straight bit fitted with a guide bearing, to ride against the template, and we had as many pieces cut as we needed - all consistently the exact same shape.