Most any auto should suite you fine - you need to decide what you want out of the high/yield/etc...the most important question that no one is addressing; is, what plants will be salt tolerant. Even if you feed them fresh water manually (which would be a pain on an island), the salt air will have a strong effect on the plants. You might want to look into that. In the marine terrestrial plant ecosystem, the plants can play a different role than on land. I would google "aelopathy", and start from there. Many salt tolerant plants evolved based on this concept due to the lack of nutrient rich soils from the coral rock environment. Make sure you don't go planting near certain plant species on the island. You most likely will need to import soil and devise a suitable watering system, as rain water may not be a useful from stemflow of other plants (i.e high salinity and TDS levels - expect pH to be way off as well).
I would make sure you do a lot of homework before you begin, as it might be a bigger battle then you expect; unless you have a strong background in growing and know how to cover all the bases.
I would look for plants that can take higher pH levels, are drought tolerant, and (sadly) have a backards leaf to bud ratio. I would personally look into Mossy's Purple AK; if I were to begin your endeavour. MI-5 would also be in the top 10. Good luck and let us know how it goes!
