You do not need to be in a faction to own a city. You need to know first that a city will decay in 90 days if nothing is built on it (At least 1 park will do). There are many facilities that anyone can build, but others like Casinos, factories, mines..etc you need to be in a faction. Some factions will allow you to join to build for a small fee, just figure out what you want and then contact different factions that can build those buildings and ask them. The government can not really stop you from building anything on your city, but they can kill your builders and make the process a headache, best advice is to contact the controlling government or faction and ask them if they have build restrictions on their planets. Also before buying a city you want to find out if the planet is shielded. Cities are really nothing more the a way to make a little income and have a ground location to store goods. I hope this helps.
On a side note, make sure you have the money to buy the RMs and production cost as well. Building a cities is a little costly to freelancers.