I don't like the feel of 1/8" for a portrait. 1/4" gives a better sense of the cut, has better weight in your hand, is easier to cut, and is stronger to support thin sections (looks like you have plenty of those). Something like this would look great in solid red oak, and I've found that material very easy for fretwork, but difficult to get very thin lines if cross-grain. It's hard to get a thin piece that has not cupped, but our local lumber yards sell 3/4" red oak cut to length down to 12" long. Menards has their random length 3/4" oak at about $3/bd-ft.
If you use BB Ply, I'd suggest, like Dan, finishing with shellac (Bulls Eye works great). Rub out the 2nd coat with 0000 steel wool dipped in paste wax- it feels like satin and the shellac gives a warm glow.
I hope you post a picture of the finished work - it looks like a great pattern, just in time for Easter.