Choosing a faction is primarily a matter of personal choice. In most cases, people choose a faction based on the school they're currently working on, often switching factions when they're working on a different school.

Once a character is fully built, the faction is usually chosen
based on the main thrust of the character and how it might assist them in their primary skills.

The factions that benefit each school, as well as their extra benefits, can be found in Define Factions and their Benefits in this FAQ.

Info by DogBreath