The 'standard' book dealing with the circus factions is Alan Cameron's Circus Factions: Blues and Greens at Rome and Byzantium and I highly recommend it, especially as it disproved so many pre-existing notions of how circus factions worked. For instance, rather than factions with clears religious and political affiliations, Cameron demonstrated that their power and loyalties were much more personal and temporary - more like football hooligans rather than organised political parties.

Roman chariot racing derived from Etruscan and Greek influences (equestrian sports at the olympics). The Circus Maximus was slowly developed as a venue over the course of the Republic, but the main image of the massive circus that is presented today was constructed under the auspices of Julius Caesar in 50. Augustus and other emperors would continue construction throughout their reigns. Tertullian discusses the chariot races and the factions in his De Spectaculis. He mentions that while the factions have an origin dating back to at least the late Republic, the sorts of factions that cause the infamous Nika riots gained prevalence gradually over the course of the empire. Nero, we are told by Tacitus, desired to be a great charioteer, a desire the historian calls a foedum studium, "a stupidly disgraceful desire". By Tertullian's time (late second, early third century) the factions were in place. Domitian would invent two factions of his own that would mostly dissolve following his death.

Tl:DR Red and White- Late Republic. Green and Blue around the time of Augustus. And there were other faction like the Gold and Purple of Domitian.