There are seven colors in CivII: White, Green, Blue, Yellow, Cyan, Orange, and Purple. If you are using the default config files (you have not modified the civ list in RULES.TXT) each color has three pre-assigned civs. Each round of play proceeds in the order of the colors as I listed them. Also, they KeyCivs are related to the Power Levels (from Pathetic to Supreme) in the same order.
Play any of the civs you like; what you chose has little bearing on what you can do beyond the setup order and the long-term potential value of being your own KeyCiv. Oh, and the Greeks are Orange in the default setup. Or are you referring to racial characteristics?