

My answer is a Model 66-3 (four-inch barrel) with a variety of .38 ammo and Federal's 158 grain .357's. But if the island is tropical, maybe I could shoot pigs or something? Snakes? Rats?
If this concept appeals to you, try to find a copy of Shirley Conran's book, "Savages." It was pretty realistic, and she consulted SAS and Royal Navy survival experts in describing what happened to a group of wealthy women who had to fend for themselves on an island off of New Guinea, after a terrorist leader killed their men. Pretty dramatic and revealing. And I don't just mean how they eventually dressed.
The handguns mentioned were S&W Chief's Special .38's, which Conran somehow managed to call Chick's Specials. I think one of her tech advisors was having a little fun with her, and she didn't know the difference.
I have never seen a book written by a woman who knew much about guns, although they occasionally manage to name one right. Alas, this is often true of male authors, too.
The male hero who taught the women to cope had an M-16 or AR-15, I forget which. He had concealed it on his fishing boat. Some Aussie bloke named Jonathon. He had a Swiss Army knife, too, which became a treasured possession of one of the women when he was killed.
The book came out in the 1980's, but is probably still in some libraries and at used book stores. I paid the whopping sum of a dollar for my copy, and it was a terrific bargain. Amazon.com probably has copies, too. And your wife or girlfriend may like it. Especially the stuff about rich corporate wives trying to outdo one another socially.
With my luck, if I was stranded on an island, it'd probably be that one off the coast of Brazil, where there are so many snakes of a type closely related to the fer-de-lance that the government bans people landing there. Their venom is especially toxic, and the island is absolutely infested with them. They've killed whole expeditions. The snakes are called Golden Lanceheads. The venom evolved to be especially toxic, to enable the snakes to kill birds readily, and eat them before other snakes take them away.
Of course, if the island really is a desert, not just deserted, your goose is cooked...well done!
T-Star