I'd say Civ4 is my favorite but it may just be that it was my first series. Worth mentioning if you've never heard of it is FreeCiv. An open source version complete with its own modding that's a bit more extensive than official releases.

I would argue each game has got more accessible with each iteration with the tradeoff being an "incomplete" game until all the DLCs are released. (Things like religion being absent in Civ5's launch)