I would bring these important basic items for a very good purpose, to keep me alive. The water purifier would bring me clean water always from the ocean, that way I can never dehydrate or die of water deprivation. Also, it gives me clean water to work with for cleaning myself, cooking, cleaning items, and various other purposes.
After I made sure I had a water filter present, I would then acquire a constant food source. It would have to be a relatively self sustaining source, that can be harvested and kept in storage all year round, and it most definitely would have to be packed with protein to keep me energized, up working, and alive. My best option I feel then would be to bring potato seeds to grow potatoes, the super food. Also, to ensure I could construct shelter and other important necessities, make a fire to keep me warm, and a object that could help bring me rescue I would gather and bring a pocket knife with a flint magnesium rock attachment to start those fires. With a kit like that Id be sure not to fail, in fact I might even be able to, if necessary, live out my whole life on that island perfectly fine.