The world of Alpha Centauri is based on a post-Earth civilisation in the stars and, as such, nationality, race or geography no longer determines what society you belong to. Instead peoples were divided amongst different factions based on ideology. Each one is distinct and has mechanical, social and diplomatic differences. A similar division in another game would be the groups in Planescape, also divided amongst philosophical lines.
The most important consideration when making a character is that it is soon enough after planetfall that your character chose to belong to this group - while there may be an unwilling population in a faction, the leaders will generally be signed up to its ideals. Exceptions can exist but I encourage you to think about playing someone committed to the cause, whether that be the pursuit of science beyond ethical bounds in the University or devotion like a worker ant to the greater community of the Hive.
Founded in the ideals of the late Captain Garland, the Peacekeepers are still attempting to enforce the Charter which the Unity was meant to found colonies on. Democratic, inefficient and sprawling, they have founded the UN council but find themselves under attack by the Spartan Federation due to their military weakness.
Further details: Peacekeeping Forces (Wiki)
There is no room for the individual in the Hive, where the community enforces absolute control in the hostile environment of Planet. A totalitarian, brutal but immensely practical society, it has thrived on Planet and now boasts the largest civilisation under which thousands are crushed into serfdom.
Further Details: Human Hive (Wiki)
Living in harmony with Planet and seeking to avoid the ecological mistake of Earth, Gaians seek a better life through understanding the secrets behind the xenofungus. Pacifistic, psychic and anti-capitalist, the Gaians have refused to terraform Planet to suit them and have instead formed deep connections to the native life, the Mind Worms.
Further Details: Gaia's Stepdaughters (Wiki)
Faith guides the Lord's Believers as they arrive on Planet - the promised land to build a New Jerusalem, far away from the sinful technology and cynical politics of Earth. Fanatical, crusading and anti-intellectual, the Lord's Believers have begun a Holy War to unify Planet, starting with the greatest threat to their might, the Spartan Federation.
Further Details: Lord's Believers (Wiki)
Hidden aboard the Unity were the seeds of Morgan Industries - the corporation which built the ship and was not about to see itself, and the potential profits of the unknown, left behind on a dying Earth. Capitalist, luxurious and rich, Morgan Industries has let comfort dominate its quest for expansion and will need to open new markets to be competitive.
Further Details: Morgan Industries (Wiki)
Mutineers aboard the Unity, the Spartan Federation are a diehard group of survivalists forged in the disastrous wars of Earth. Power, discipline and expensive weaponry have enabled this faction to dominate the Planet so far, though fighting wars against the Peacekeepers and the Believers is starting to exact a terrible toll.
Further Details: Spartan Federation (Wiki)
The University came to the stars to unlock the secrets of Planet and nothing will be permitted to stand in the way of progress. Intellectual, elitist and open, the University has begun a great project to clear part of Planet of the fungus to permit the mineral development required for their research.
Further Details: University of Planet (Wiki)