Wow, a lot of people outright banning all religions here, I would create a religious freedom within reason, and since I am the dictator I get to decide what is reasonable.
I would build an awesome stone castle in the centre of the Island that would house me and all my advisors and all civic functions. The island would be powered by a hydro electric power, wave power, and solar power.
The economy would be capitalist based with all social aspects socialised eg. healthcare, education.
To keep it corruption free everyone would be personally answerable to me, so double-dealing politicians? DEPORTED. people abusing social care? DEPORTED People scamming or blackmailing? DEPORTED. Major offences that deserve punishment (murder) would be locked up for life, with bread, water and no other comforts.
We would be a small island, between 50 000 and 100 000 people, but we would import as little as possible, and all businesses would be local or island-wide. (no trans-national companies unless we start them.)And we would get money from other countries by exporting our raw/produced materials, and through tourism.
EDIT: 100th post woohoo