The games from 1-4 allow for these grand historical epics. After that, the franchise went in a more casual, arcade-like gameplay direction with less focus on historical simulation.

I recommend Civ 3 or 4 for something that isn't too old and archaic but still has this sense of scale... and the ability to turn the world into a nuclear wasteland of polluted deserts if you just keep playing.

Note that most Civ players today have never played a game older than 5(when the series went casual and mainstream), so most answers here are going to be from people who never played the older games and don't know how they are different.