I finally designed a piece of furniture in the CNC & Sketchup software that actually cut & routed accurately enough to fit together! Lots of trial & error.
I got some 1/8" baltic birch plywood for about $1/sq' - I probably won't be using it for furniture anymore as it requires a bit of sanding, instead maybe use it for dollhouses/roomboxes.
For furniture or smaller items - poplar will work, but cherry is even better. I have an old cherry table-top I need to slice up into thin stock.