I prefer the look of 1/8" BB ply, but cut 1/4" as well. I don't think I would go much larger than 1/4", though. If it's thicker, I think you lose some of the detail since the edge of the wood would cover the backer at certain angles (the backer really makes the portrait stand out so you can see the details). The real trick with cutting 1/8" ply is to stack cut 2 or 3 pieces. It gives you a lot more control over the blade. Plus, you get 3 copies. Even if you don't want the extra copies, I'd still stack cut just for the extra control. It may seem wasteful, but the end product is well worth it.