Ginger had her own theme song, so she is out (I wanna be loved by you).

All three women had a theme song when they formed their own trio (the Honeybees) with the hit "You need us", so for theme song consideration, you have to exclude the women.

The guys were never any good with music, although once in a while Gilligan did okay on his makeshift bongo set (a carryover from his time as Maynard). I believe even the Professor did a couple cameos with the bongos as well.

In any case, we're talking theme songs here, not who you'd want to remain on the island with.