Must haves
Israel/Hebrew: As a people they have had a huge impact on other civilizations starting with rome. Judaism as a religion already represents this impact in the game and is included when for example sikhism with more adherents is not. But they have never had a lasting empire and have ruled only over a very small area for limited periods of time. The truly remarkable aspect in the people is that they have survived as a small and often persecuted diaspora for a very long time, it is not their success in empire building.
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Starting with Rome? Try: Babylong, Perisa, Egpt . . .
About not having a "lasting empire" certainly not like Rome, but they've been around for over 4,000 years. Civ isn't just about "empire" building, it's also supposed to be about culture, religion and technology. Of course, my favorite part of the game is empire building. . .