I will gladly come down and help you establish a lawn if I can stay at your house free of charge!!!! I don't need much space, but you will have to feed me :). The first thing you need to consider is water. Establishing a lawn, from either seed or sod, will require a lot of fresh water, especially with your sandy soil and hot windy climate. Will this be a problem for you? If it is a problem, or too expensive, then it will make a lawn somewhat difficult. It might be a good idea to become friends with a local golf course superintendent, as they will have plenty of information as well as sources of things like fertilzers and amendments. In terms of what type of grass I think you should consider paspalum. Paspalum is a salt tolerant grass that spreads well and does best when cut short, like a golf course fairway. It can be grown from seed or sod. Are there any sod farms on your island? If not, sod might be very expensive. Again, a golf course superintendent might be your best source. When establishing a lawn, the best results generally happen when you start from scratch. This requires killing whatever grass/weeds you have with a herbicide, and seeding a few weeks later.

P.S. Your English is very good, much better than at least one member on this forum.