The pilot stated that during approach for landing at the 1,840-foot-long runway, the airplane's airspeed was higher than recommended for a short field landing. He stated that after the first touchdown, the airplane bounced and floated, then touched down on the runway a second time and bounced again. The third touchdown was "firm," the airplane became airborne, and the pilot elected to conduct a go-around. The pilot returned to his airport of origin, and postflight inspection revealed damage to one propeller blade. Further inspection revealed substantial damage to the engine firewall. The pilot reported there were no mechanical malfunctions or anomalies with the airplane.