What sort of tech level is available? Are we talking a very early colony with not much higher tech than we have now? (ie, need to be super strict because it would be very easy for a malicious or even clueless individual to seriously screw everyone) or way beyond that so that's not so much a worry?
Hard science fiction, pretty much. Hydroponic farms, meat-vats, and algae-vats for food, more-or-less modern life support systems (possibly assisted by cracking lunar rocks for oxygen), et cetera. Good enough to be self-sustaining, but no magic nanobots, FAI, or anything like that.
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?