External screen capability is really important. It won't be used much for control, but if you can get a projector (say, sneak into a unused classroom between classes...), some good live scoreboards can be shown. Again assuming OMAP35xx, we've got a video out interface; it would be foolish not to have a connector.
So I'd say either a Beagleboard or a Gumstix Overo (from what I've seen) for the main board.