The student pilot was landing the airplane in a crosswind and reported that on final approach a gust of wind pushed the airplane to the right of centerline. As it crossed the runway numbers the pilot applied “too much” back pressure, the airplane ballooned, bounced, and settled onto the runway. The airplane then began to veer to the right, and pilot attempted to correct the movement but overcorrected and the airplane veered to the left into the grass. The pilot realized that the airplane was not slowing, applied “more pressure” to the brakes, but the airplane proceeded down an incline. The nose landing gear then collapsed, and the airplane nosed over coming to rest inverted resulting in substantial damage to the fuselage cabin, rudder, and left wing. The pilot reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation.