I would be all about survival at this point being Lost on the island. I would at least check the cave out, and, after seeing it, I would definately be staying there instead of on the beach. Gotta get rid of those bodies, however. Maybe stand them up outside the narrow entrance to warn others away.
I voted caver, as there appears to be adequate shelter from teh ebil Daystar and much fresh water, but I see no reason why we couldn't work the beach in shifts.