It depends. ;) Here are my thoughts:
Civ 1 - very dated graphics and UI, atrocious AI, brilliant concept, but crude excution in many aspects. I'd recommend against starting with it, it has no advantages over the others. It is less complex than Civ3 or Civ4, but so is Civ2.
Civ 2 - Probably a decent point of entry. Gameplay is less complex (and therefore less overwhelming) than the later Civ games, but on par with Civ1. Graphics, presentation and UI are _far_ better than Civ1. The AI is still very bad. Many crude gameplay mechanics from Civ1 are still present.
Civ 3 - Further improved presentation (though some well-loved elements from Civ2 are missing, notably wonder movies, and advisors played by real actors). Gameplay is more complex, but also introduces new problems (corruption as a very non-fun new game mechanic, overpowered artillery). Decent AI for the first time in the series.
Civ4 - Definitely the most complex game in the series, also the one with the best AI. Most gameplay issues from the previous game have been ironed out. The UI is very good too - while the amount of information can be overwhelming at first, it always gives you the information you need, especially if you improve it with the BUG mod.
Civ 5 - Not really a Civ game, but rather a failed mix between Civ and a wargame (like Panzer General). Gameplay has been simplified a lot, but isn't working as well as the previous Civs. The AI is back to being atrociously bad. The UI is a clickfest that hides information when you need it. Players are forced into pre-designed playing styled by removing choices during play. I'd stay away.
Conclusion:
I recommend to start either with Civ4 or with Civ2. Civ4 is the more mature game, but also more complex. If you're okay with the idea of playing a couple of games before you truly understand all the concepts, then choose Civ4. If you prefer to start with simpler gameplay, choose Civ2.