The student pilot reported that the flight was his first solo cross-country, and the arrival and departure at his first airport were uneventful. About 8 miles from the second airport, he listened to the airport's automatic weather observation system, which reported that the wind was coming from 020° at 5 knots. He entered the left traffic pattern for runway 34, and while on the downwind leg abeam the end of the runway, he reduced engine power to idle and lowered the wing flaps to 10°. He then turned onto the left base leg and maintained 70 knots and lowered the wing flaps to 30° on final approach, maintaining an airspeed of "between 50 and 54 knots." At the runway numbers, he began to pull back on the control wheel to initiate the landing flare. The airplane's nose then abruptly pitched up and left, which he believed felt like a wind gust. He tried to correct by releasing back pressure on the control wheel and using rudder and ailerons to move back to the right, but the airplane was still left of the runway centerline. Subsequently, the airplane bounced hard numerous times, the propeller struck the runway, and the airplane then departed the runway to the left. During the runway excursion, the nose landing gear collapsed, and the airplane skidded across a taxiway, eventually stopping in the grass. The fuselage and firewall were substantially damaged. The student pilot reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation. Review of the Pilot's Operating Handbook indicated that the airspeed for a normal landing should have been between 60 and 70 knots with the wing flaps down.