If its just to be a floating island I'd use a used barge. Plenty big! Then I'd hire a tug boat to park it somewhere in the Philippine Islands where there aren't too many Muslims (easy to find) and its surrounded by real islands for protection and in good fishing grounds. Perhaps off Camiguin Island.
http://en.wikipedia.org/wiki/Camiguin Since its a barge you could load part of it up with dirt for veggies and save rain easily for watering plants, drinking and showering. Water might be a problem if it forgets to fall from the sky. Global warming is supposed to make more rain here and we get a fair amount already, usually in a tropical downpour and then it clears up.
Then you will need some solar power panels and a bunch of car batteries to charge all day and use at night. Also gives you a way to refrigerate food though that takes a lot of solar panels. You could salt dried fish easy enough but then you have eat it, yuck.
You'll need a solar cooker. Like an old style medium satellite dish lined with aluminum foil. That's about the the cheapest solar cooker out there.
You definitely want a hookah dive system which is a regulator on a hose which runs to the surface where there's a specially made 12V compressor that will pump clean air down to you. I got mine for $900ish iirc. That will allow you to go down and set and check fish traps. You'll have to grow some bamboo on your barge in order to make the traps. Metal traps that are left at sea will trap fish long after the owner has forgotten or lost them and that's just bad. Bamboo will break down.
The good news about this is that you will be in the Philippines so you'll find a nice girl that will talk you out of it.
I never used the hookah dive system I have until a few projects are finished and I can build my sailboat. This link is not to the kind I got but just to give you the idea. Looking at it this one takes you pretty deep. If you go as deep as they say you need to get a dive chart that will tell you how to avoid the bends. You can find that online.
http://www.scuba.com/scuba-gear-152/Hookah-Systems.html
Wait that one has a gas engine and is spendy...but takes you twice as deep as this one which is 12V and cheaper. This is the one I have.
http://www.hookamax.com/17710.html