Free market is free market, you cannot force people to use 1 currency. If they are truly libertarian (which i think they are) then they will use the currency which is the most secure and prominent: Bitcoin.
What if they are libertarian but not tech savvy?
Bitcoin is great, but requires you to have a smartphone and use an exchange to get coins. Maybe in future when hardware wallets are cheap and easy to get and you'll be able to get BTC from an ATM across the street it will actually be available to everyone.
I`m not sure but first they will need an army and a police force, then people will move it and build houses, canalization, and water system.
Then after the basics are done, you can build the economy, and since its a free country, no permits and regulation are required to set up a Bitcoin Atm
So i`m sure after the basics are built, the place will be full of Bitcoin ATM, people selling goods on the streets, without permits, and with low or no taxes.
Man it sounds like a paradise on Earth