Ned,
Back in the day Bullseye was a revolver game. Smith and Wesson was a common gun used, use a K-22 (M17 or M617) or a K-38 (M14).
While you must reload, it is not while being timed. Standard speed loaders will work fine.
At our club some of the guys shoot two handed. These are the older guys that have developed poorer eyesight or the shakes, as well as some of the new shooters. Once these shooters start to get decent scores they change over to one handed shooting. My point is most shooting clubs will be tolerent of a new shooter.
As well I have shot with revolvers and find no serious disadvantage. It is more challanging. When I am shooting PPC during the winter I sometime shoot my PPC revolver (S&W, M686) double acton, during a bullseye match.
Much is available on the internet, and stop by your local club to watch. Most places will be friendly.
Enjoy,
Fred