The student pilot reported that after landing on his unpublished airstrip, he did not get the airplane slowed down on the wet grass surface. During the landing roll the airplane slid sideways, and the pilot aborted the landing. During the departure climb, the left wheel struck a fence resulting in a loss of control and the impact with a storage structure. The airplane sustained substantial damage to both wings and the horizontal stabilizer. The pilot reported there were no pre-impact mechanical failures or malfunctions that would have precluded normal operation.