I would use the #8, 1 1/4" length, flat head, square drive, SS screws. This will give you a penetration of aprox 1/2" into and through the studs. Make sure to predrill the holes to prevent cracking the trailer's extrusions. In the soft pine/spruce studs, you shouldn't have to counter sink the heads. The screw heads should pull flush so they are not proud of the surface.

The #2 square drive is much less able to strip out during the driving, than a phillips cross point bit. You can apply much more torque.