So hard to pick a favourite, II, III and IV all gave me a much needed escape from hard times in my life, but I'd probably say Civ III just because that's probably the one I have the fondest memories of and also I believe that was the first time culture/cultural victories were introduced to the series. It seems almost an afterthought now, but at the time it really added a whole new level of depth and strategy to the gameplay.
I remember doing a game with the Chinese on that particular iteration of the title. It was a Huge continents map I believe, but I started isolated on some tiny little island. I spent a fair bit of that time building an army and after the first two-thousand years or so finally made contact with the outside world. I remember you could transfer ground units from one naval vessel to another without the receiving naval unit losing its turn (a little exploity perhaps), so I strung a bunch of triremes across the ocean (via Great Lighthouse wonder, I think) and shipped my whole invading force double-quick onto the English coast. I let them keep their last city
I also had a couple of cities on another continent that Ghandi of all people invaded and seized. I sent a force over and, rather than keeping his captured cities, razed half of India. He had a continent spanning empire so it took some time, but fun all the same!
😉
Unfortunately, my computer borked up sometime after that, but I'd probably say China are my fave civ based on that game alone.
Sorry to ramble, but it's fun to reminisce!