Design your government and tax system. (Anarchy, minarchy, actual signed social contract, townhall democracy, etc)
A single leader who proposes decisions. For every decision there is a referendum, for which every citizen has the right to vote. This leader would be changed weekly - the next leader would be chosen by random from the citizens who have been leader the least number of times. I, as the founder, would be the initial leader to get the ball rolling. We would start with no laws and no taxes but these may be introduced if proposed by the leader and agreed upon through referenda.
Design your monetary system. (A new fork off bitcoin, bitcoin itself, modified peer to peer currency, Gold, etc.)
No money initially but it may be introduced if decided upon by the democracy. Instead, there would be an understanding that everyone works if they are able and works in the areas in which they have strength. The goods of the labour should be shared between citizens as per need. Durable goods that are not needed can be saved for the future. Excess perishable goods can be shared equally between citizens as a reward for collective hard work.
If someone is able to work but refuses, other citizens may raise the issue with the leader. The leader can then decide to remove the citizenship of the person and there is a referendum on this decision. Without citizenship, a person loses their right to vote and be leader and loses their right to access the goods of the labour, although citizens are within their rights to share their own share of the goods with this person if they so wish. If this person reforms, then the reverse process can happen and they can be reinstated into society.
Significant variations from today's laws that you want to note (intellectual property, personhood laws, etc.)
No intellectual property or any other laws unless decided upon by the democracy.
Any other individual quirks you'd like to add ( Entry for hot girls only, Everyone speaks a new language, anything that strikes your fancy)
Initially I would only allow people onto the island who are both able and willing to work because a small society could not support many people who don't work. Everyone should be fluent in a common language because communication is vital. This common language would be English for the simple reason that it is the only language that I can speak fluently. Initially, everyone would get weekends off and there would be 12 holiday days in a year - the solstices and equinoxes and the 2 days either side of these days. Initially, working hours would be 10:00-13:00 and 14:00-17:00. Obviously, all of this would be subject to change if the democracy decided.
What would you do to convince productive people around the world that they will be better off if they come to your little island compared to wherever they are living right now?
I'd broadcast the benefits (probably over the internet) - the true democracy; the freedom; the strong sense of community; the short working hours.
There are probably some flaws here and this society wouldn't work at a much larger scale but is suitable for a small island. However, our current society has many flaws anyway and I believe that this fantasy society would be better.