Great thread -- reminds me of one of my favorite movies:
Cast Away starring Tom Hanks as a guy who gets stranded on a deserted (not desert) island and has to figure out how to survive. Among the problems he had to deal with was loneliness -- so he made friends with a volleyball named "Wilson".
To answer the question: I think, since the island has very little rain (desert), I'd go with some kind of general purpose tool that would help me catch some fish -- maybe a knife that I could attach to a stick to make a spear. But if the island has little rain is there a source of fresh water? If not, chances of survival are nil.
But if there is fresh water then agriculture would be possible. Which brings us back to the Sporke. I'd bring that as well as a variety of seeds and fertilizer.