My choice of 18 initial civs would be distributed as follows:
European;
Greece
Rome
Germany
England
France
Spain
Eurasian;
Russia
Turkey
Middle Eastern;
Persia
Arabia
Babylonia
African;
Egypt
Abyssinia
Asian;
China
India
Siam
Americas;
Aztecs
Sioux
The reason i picked the above civilizations are based on their impact on world history in general as well as fairness to all regions bearing in mind the distirbution of world population through different chronological periods.
Babylon, Egypt, India and China are the cradles of civilization where mankind first settled down and built their villages.
Greece, Persia and Rome were the next step in humanity as they built cities and empires where civilization advanced.
Germany, Spain, England, France, Turkey and Russia were undoubtedly all superpowers at one point in history, all of them having vast, multi-ethnic, multi-religious empires that stood the test of history for hundreds of years. They ruled simultaneously over most of the known world.
Arabia, under the banner of Islam dominated half of the ancient world and threatened Christian existence for hundreds of years being the first teocratical empire in the world in which they replaced tribalism with the notion of religious brotherhood. During the darkest hours of Europe, Bagdad was the capital of enlightenment, freedom and prosperity with Islam entering it's Golden Age.
Abyssinia is not only on the list to represent black Africa, but i believe they are also a much better candiate than Zulu's, whose only major achievement known in popular culture was to win a single skirmish against a British expedition. Abyssinia, which is a more historically accurate name for Ethiopia, having the chance to interact with other civilizations did indeed develop a unique substantial civilization which was able to preserve herself.
Siam was meant to represent all of south-east Asia and I believe, not only because of their amazing culture, but also for their interaction with China, India, Ottomans and Europeans throughout the ages, are a better candidate than Japanese, as Japan has only been open to the world for the last two hundred years. Japan, of course deserves a distinct place in the history of civilization, however, given the restraint of 18 civilization cap, it would be fair to select Siam due to her culture being far more different than Chinese when compared to Japan and also the human populations they ought to represent.
Aztecs are in the list for having the strongest empire in the known world before the conquests. Incas would also be a good selection if we weren't limited, but instead i selected Sioux to at least represent North American people. It could as well be any other native American tribe here as I am only trying to be politically correct, because I don't think they had achieved any progress throughout history that we would consider in the top 18 civilizations. I would personally enjoy the Vikings more and have the natives as barbarian villages.