An 1 GHz iMac G4 will not run Puma. It requires either Jaguar 10.2.3 if it's a 17in or 10.2.7 if it's a 15in. I would put Tiger on it as it provides the best balance of speed and compatibility with applications IMHO. Leopard will support more and newer versions of applications and games but will be on the heavy side due to the GeForce4 not supporting Core Image, thus my recommendation to stick wih Tiger. Jaguar and Panther aren't really worth it as you'd be stuck with much older applications (and games) when using them - the glaring exception to this, though, is running OS 9 games in Classic, which will be much better in Jaguar than in Panther or Tiger.
How much RAM does the iMac have? I'd recommend to max it out if it hasn't been already.