Single Board Computer for custom gaming device

Hello, everyone first post to the forum

i am in the middle of starting my christmas gifts for family. every year i build them something. this year i am going to be building a handheld MAME cabinet hopefully in the original nes controller.

Im trying to find the smallest computer possible so i can use the controller. i am looking at using one of the PowerPC single boards and was wondering if anyone has any suggestions.

the board doesn't need to be anything close to fancy. the only things that will ever be plugged into it are; a screen around 3 inches, some sort of memory(ssd-cf or mem stick) and one usb port to be able to use a nes to usb converter so i can still use the same buttons. I am just going to be using the lowest impact linux distro i can find as the only thing it will ever run is nes and maybe snes roms through MAME

size is the most important part here not power. if anyone has any suggestions it would be greatly appreciated.

-I am willing to deepen the controller to give me a bit more room but i want to deepen as little as possible.

It sounds like a much better, and easier, solution would be to use one of the so called NOAC (NES-On-A-Chip) devices that they sell online and in various catalogs. These are single chip boards that completely emulate the NES, many of which still have the traces to connect a cartridge slot to it.

Pairing one of these with a collection of NES ROMs (I know there are some re-writable NES cartridges out there, but I don't know the price point) should prove to be much easier developing a whole mini-distribution just for running an NES emulator (besides which, I have found most emulators for Linux to be lacking anyway).

i have been thinking about using one of those instead but i can't find anyplace where i can get them; as i live in bc, canada. all the sites i found don't ship to canada and the closest place to me that i know has them is the west edmonton mall which is a good 13 hour drive away...