Which lock do I need? (*pics* Please help, 5 stars for best answer)?

Leave that existing handle and lockset in place. Get a deadbolt lock with a keyhole on one side and a knob on the other. Also get a deadbolt install kit that has a holesaw for installing the lock. Probably around $25 for both. You'll need need a drill, a chisel, a 7/8" paddle bit, a #2 Phillips screwdriver, and a tape. Instructions are included with the lock.