I'd establish a constitutional monarchy, where the monarch is the head of the judical branch and the executive branch would be a senate with elected senators. The legislative branch would be devided amongst judical and executive. There would be a constitution which can only be altered by direct democratic vote. The government would not have the ability to levy taxes or other fees. The position of monarch would be tied to land ownership of the majority of land. The senate would be unpaid. Police and military would be directly funded by the local community as they see fit. There are still a lot of bugs in this system because it's not really fleshed out, just an initial thought.
You are now in control of a habitat on the moon. It has no ties to any government; its creation was funded by a wealthy philanthropist who just wants people to emigrate from Earth. The cost of doing so is within the reach of a middle-class family if they sell their home; you can therefore expect a decent number of immigrants.
What sort of government do you establish? How do you go about ruling so that your new settlement on the moon will survive and thrive?