Everyone is right, technically being a host computer only needs to be able to serve up the raw data to the Apple TV which requires little to no processing power. With that said, I would hesitate to recommend anything less than an Intel based Mac Mini IF you don't already own a G4 mini. My reasoning is two fold:
1. A G4 Mac Mini is extremely old 5+ years which means it could die soon.
2. At any point in time, Apple could stop supporting iTunes on a G4 and require a newer version of iTunes for Home Sharing to an Apple TV (i.e. new firmware requirements on the unit). Thus rendering the G4 Mac Mini useless.
However, if you go with a Core Duo based, at least you know you are covered thru Snow Leopard and thus should be able to run iTunes for a very long time on the Mac Mini.
Again it isn't the processing power of the unit I am concerned about, but G4 architecture being rendered useless by software upgrades.