It's not high end so it really doesn't matter.
I would use whatever scrap that's big enough laying around.
3/4 maple ply (descent cabinet grade) would be my choice. Core is good enough to rout those profiles and v-grooves. A little putty if you hit a void isn't going to show with 19 coats of paint. :)
Mdf would be 2nd choice.
P.B. in a bind, before buying a whole sheet of something else.
Figuring out how to do something you have never done is what makes a good challenge.