The student pilot reported that he performed practice maneuvers over a field for about 20 minutes before returning to the airport to practice landings. After becoming established on final approach, the airplane touched down "on the numbers," then proceeded to bounce with ever increasing frequency and severity. The airplane departed the runway surface, the nosewheel landing gear collapsed, and the fuselage was substantially damaged. The student pilot reported no preimpact mechanical failures or malfunctions with the airplane that would have precluded normal operation.