According to the pilot of the Piper PA-28-181, following an uneventful flight, he approached the destination airport. While turning on to the final leg of the traffic pattern, the pilot saw an airplane pulling out from the apron and onto the runway. The pilot elected to make a 360-degree right turn in order to provide additional space between himself and the other airplane. He then continued the approach, but "came in too high and therefore floated too far along the runway." After touching down once, the airplane "ballooned," then contacted the runway again "hard." With insufficient runway remaining, the pilot decided to go around. As the airplane accelerated, the pilot turned the airplane to the left to avoid striking the trees ahead of him; however, the left main landing gear struck one of the trees, and the airplane subsequently impacted the ground.