You're the mayor. That means you've got to have someplace to do all the important decision making things that you do everyday. Enter: the town hall.
Town Hall
The town hall is an important first step in the life of a young city. It's your personal headquarters. Your office. Your throne room. Your prison. Once built, you can change the name of your city if you choose and it grants you access to some of the more important ploppable services you're going to be using.
City Hall
Your first upgrade for town hall is to boost it to the level of city hall. When you upgrade -- which you can do from the government HUD -- the building will retrofit itself with a brand new marble facade. You will also be granted the first of your many department modules.
City Hall is going to get quite sizable. In the image above, I stacked as many of the six departments on top of each other as I could, but notice that the department of education stands alone in it's own building. You know how professors are -- so full of themselves.
Module: Sign
Just in case there's a sudden rush of people building with marble and your city hall becomes lost among the weeds, you can plop a crazy-big sign out in front of the building so your citizens can distinguish your building from, say, that of the 4th-century roman emperor who moved in across the street.
Department Coverage
For each of the following modules, bonuses and unlocked buildings are in effect for every city site in the region once any one city site has it. That means if one city hall has all the departments, the other city halls in the region don't need to bother building their own. This is a huge space saver and a reason to "specialize" in government and politics.
Department Module: Transportation
This is the department I would go for first because it's most important features is that it allows cities in the region to share Sims via a network of train stations, bus terminals, airports, and docks. Diminishes the costs involved in your transportation system.
Department Module: Utilities
I'd go for this one second, as the water towers you've been using will eventually run dry and you're going to want to have the pumping station when they do. Improves the coverage and efficiency of your utility systems -- namely power, sewage, and water. It also unlocks the sewage plant and recycling centers.
Department Module: Finance
Boosts your tax revenues and allows you to micromanage your tax rates based on class.
Department Module: Education
Gives a boost to your education system and it's effects on your Sims -- rocketing them upward from retarded mooks that regularly set themselves on fire to snobby erudites who know what the word "erudite" means. This department is required if you want a university or a high school -- and you do.
Department Module: Safety
Boosts your police, fire, and health services -- speed, coverage, and effectiveness. Once you plop this one down, you'll be allowed to use the hospital, large fire station, and precinct.
Department Module: Tourism
Effectively drives your tourism industry by generating tourists who arrive via train, bus, and ferry. You also gain a bunch of cosmetic/tourist-attracting buildings, including landmarks, stadium, and parks.
Module: SimCopter One
Allows you to fly around the city and to/from your mansion -- once you own one, that is. Of course, a real mayor would use the subway to show that he or she is one of the people. But since there are no subways in SimCity 5, your version of the gas guzzler is acceptable.
