There was much good advice in this thread, but you will also want to look at what your ambitions are in the game. If you just want to be an average joe and build your nation, that's fine. If you want to become important in the game, the primary way to do this is taking up the politician's trade.
CTC, for example, is an awesome alliance to get some in game training... brilliant minds over there, and you will have a powerful nation quickly. However, CTC in itself doesnt offer anything in terms of advancement, it's more like an academy of sorts... after finishing there, you can move on to a number of other alliances and you'll have the knowledge and credentials to join mid level administration (training, aid coordination, etc). There you can work your way up.
If you want to get into the political game, the best thing to do is join a mid sized alliance... 1-4 million NS is a good rule of thumb. These alliances are generally large enough to have competent govt and firepower, but small enough to allow room for advancement within a relatively short time. These alliances often have a shortage of diplomats so that's definitely an excellent place to start; if you show some skill you'll win elections or be promoted in time. They also often have a friendlier and closer atmosphere (like a community college compared to a major university).
Also, don't dismiss nondemocratic alliances off the bat. There are good democracies, but in some cases they are corrupt, highly inefficient/bureaucratic and filled with internal politics and strife. Of course, can also be true of dictatorships, triumvirates, and other forms of government. If you are good at PR and electioneering, democracies might be what you are looking for though, if you are good at being popular. Do some research on alliances, and better yet, join IRC at coldfront and ask people.
If you want the opposite of a democracy (i.e. military command) pick NPO, poison clan, or other similar alliances. Be aware there are halfway alliances too.
Some people like so-called OOC (out of character) alliances based on real life politics or activities. They can be fun and have a club like atmosphere, but unless they are based on gaming (like TOP), I would avoid them if you want to be a serious government type or want to play the game in a traditional IC manner.
Be aware of the color teams of alliances as well. Every color based alliance has color politics and various levels of interactions, friendships and rivalries with other alliances. Aqua, orange, purple and blue are very united color teams; while green, yellow, white and especially black have experienced strife in the past. Red belongs only to New Pacific Order and the anti-NPO revolutionary group Vox Populi.
These are just a few considerations, but best thing to do is hop on coldfront.