So you haven't played a civ game from civ 2 onwards? I still desperately want to play civ 2 some day, but I've been playing almost religiously from civ 3 onwards (played the first a buttload as well). I'd like to recommend Civ IV which I'm tempted to say is the best one in the series, and definitely I think easier to get into than the original, mostly because the original's interface is almost unbearably archaic at this point. I'm not too sure about it being the best seeing as how Civ V is brilliant as well, only they went kind of haywire with the religion aspect, I miss corporations, and the one unit per tile limit, although an improvement, needs to be tweaked some more.
One of the things that is so great about Civ IV, which I for some reason stupidly avoided like the plague for a long time, is the collection of scenarios. Basically it is the Civ experience condensed (not that it takes any less time to complete) to some particular timeframe or setting where you don't have to worry about tech trees and advancing through the technological ages fast enough. For example, one scenario the entire map is only the north eastern part of Africa and a bit of Asia where you fight for resources and trade revenue, while others only another only focus on the campaigns of Genghis Khan / Alexander the Great, and yet another one only focuses on some conflict in medieval Europe. There is also an awesome scenario about viking raids on the British Isles and western Europe, a cool one about colonial times in America, a brilliant historic one set in Japan, a ridiculously complex one about WW2 and at least one weird highly acclaimed sci-fi one. Of course there are also scenarios set in ancient Rome and Greece, which are perhaps my favorites.
Civ V also has some very good scenarios, and last time I checked there was even one where you could play as the Boers / Zulus in South Africa, which was awesome!