If you're making a portable you probably need something to watch it on. (Unless you want to guess what's happening in the game, but I wouldn't advise that) Anyway, this forum is your "Hacking a pocket TV/screen" one-stop solution. Share your experiences and knowledge here.
You can use 4 rechargeable AA batteries with pocket Tvs but not with screenpads; as far as I know they require at least 6volts. So if you make a portable whose console uses 5volts you can run the whole thing on 4xAAs(as long as you use a pocket tv as the screen).