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?
A 'technocratic' Bureacratic Despotism, with the Philanthropist technically in charge.
Before you say otherwise, realize that the OP has asked: "What sort of government do you establish?", not "What sort of government WOULD you wish to establish?" Regardless of my personal views, the wealthy philanthropist has too much influence and control over the government (by being its sole source of funding) for it to be truly 'democratic'. I also have to make sure that the system survive and thrive, so I cannot rely on testing out new and exciting ideas, lest the philanthropist sues me when they fail. The safest method for surviving and thriving then would be to rely on a bunch of technocratic experts to handle the government for the philanthropist, and if the government collaspes, it would be the technocrats who are blamed, and not me.