I use 1/8" red oak, cherry and mahogany to cut butterflies out of and as JT said 1/8" or 1/4" BB plywood. To start with I would stick with the plywood as it is much more stable than the clear wood. Let me know if you would like a number of online sources to buy wood from. Mick.
While the 1/8" ply is thin and can be hard to cut because if that, we often tape 3-4 of them together and attach one pattern and cut all of them at the same time... that is easier to cut and you end up with more done for the same amount of work.