I've ended up with all the Civ games, but the last one I played properly was Civ2. (And I was never particularly good at it.) If I were to play one now, which would you recommend?
A history of Civilization is a bit funny, as they were constantly experimenting with rules and feature design, sometimes changing core mechanics in updates, and when you think they finally reached something concise they surprise you by resetting everything in the next game.
Curiously, Civ2 is often regarded as the "best civ game", even though it had numerous bad design decisions (some of which transferred from Civ1). Maybe because it was simple and its flaws could be tolerated for simplicity sake. And it created truly random worlds with bizzare land patterns.
Civ3 was first one made by new developer (Firaxis), they introduced very interesting concepts: trade requiring actual routes rather than caravan units and trade goods having distinct effect on game; also first game featuring state borders, so finally opponents could not randomly wander a settler into your land

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Civ4 iirc was the last one featuring giant maps and empires, and also last one that had rectangular tiles. It had 2 big updates, and main game combined with both updates finally made a pretty logical system of rules, from what I recall. It was the first game where you could upgrade units with perks as they leveled up, allowing you to create extremely powerful veteran armies (so long as they stay alive).
Oh, and, it was also first fully moddable game, introducing open XML-like scripts, and people were creating all kinds of mods and total conversions with it. You could go into the data files, change few dozen of strings and create a completely new terrain type with it's own bonuses for your game.
Starting with Civ5 there are hex tiles, and maps became smaller afaik. Also combat rules changed again. There appeared to be units that shoot at range of x2 hexes, siege units that can only attack cities, and cities had garrison that may attack sieging units on its own. Culture became more important than ever (culture appeared first in Civ3, and its effect on the game gradually increased since).
I did not play Civ6 but I heard that maps are even smaller, and it is more focused on managing small states rather than doing endless conquest in Civ2 style.