Well, that somewhat depends on what you're looking for.
Absolute beginner? Try Civ Revolution. As has been said earlier, its quite watered down compared to other Civ games.
Working your way up, Civ V would probably be the next most simple to learn the mechanics of. It doesn't have the same depth as Civ IV in a lot of aspects, and the combat is easier to recover from if you make a mistake [In Civ IV if you attack something too powerful without thinking, you'll either win {By a miracle}, or lose your unit. If you're using a unit with a withdrawal chance you might have a 10% chance of running away, but that unit is basically dead. Civ V attack something too strong by accident and you're unit will be damaged, but you'll be able to run away and hide in the same turn, and that single attack isn't necessarily the make or break for your unit].
From there Galactic Civilizations 2 is alright. Somewhat different to the other games mentioned in my post, but its still quite good. The campaign can be brutal, even on Cakewalk, however normal matches against the AI are piss easy {On cakewalk} if you have even a basic idea of what you're doing. The ability to design your own race and ships is an added bonus.
Next, my personal favourites: Civ IV and Medieval 2 Total War.
Civ IV is the predecessor to Civ V, but is more complex in a number of respects. Get the Beyond the Sword Expansion for it, and it gets even deeper, but is still manageable if you know what you're doing. Beyond the normal researching, founding cities, managing religion, being a part of the UN, choosing your civics and building a military to pound your enemy into Oblivion, you now have to worry about Espionage [Not a lot, but it can be useful for you or your enemies], Religion based UN for early game [Forgotten what this was called
] and Corporations. On top of that there are many amazing mods for BTS including the Fall From Heaven Series [Age of Ice included on Disk, FFH2 available for online download and install].
Medieval 2 is a bit different. No research. You don't have to worry about it. Technologies will just appear as the game goes on. You cannot found cities, only conquer ones already existing. However, each of the buildings you build in your city has the effect of a technology tree [For that city], the battles occur in real time, and you command your units using tactics [Which hopefully you are good at] and you have the Papal states to worry about [They are your best friend if you're on good terms with them, but if you're on bad terms you're basically f***ed]. You also have your Royal Family to worry about.
Both games include heavy utilisation of your races military resources, diplomatic negotiations that can and will heavily affect how your game goes, economic management that will make or break your empire and political management that can grant you bonuses, or be a hindrance, dependent on how you play.