Well from what ive read here most suggestions seem t be focused on tiny islands and barren expanses of land, but ofcourse they all are claimed by one nation or another and the likely hood of anexing any is rather low.
my suggestion would be to forget about trying to adquire any of those islands and to instead focus on unclaimed region. it may sound unfesible but im my opinion the best option would be to claim a table mount, bank or guyot, there are quite a few that are located within 0 tp - 20m (with expanses often 10+ km wide at such depths) in depth in international waters. and i suppose that the investment of placing stilts or a floating structure would be way less than trying to buy a strip of land from an existing nation, plus such settlement would be open to economic development based in sea industry.
another less desirable prospect would be to claim part of Marie Byrd Land, and settle near exposed ground, the sea can be harvested for food, energy and construction materials.
i know none of my ideas are the idylic white sand beaches most would like to settle a hedonistic nation (well maybe an equatorial sea mount might do) but imho they are the most realistic areas to place a settlement without legal hassle.