Back when I was looking for my first deity win, I found I improved my starts a lot by reading the games in the 'Legendary Games' archive, the SG's all are detailed reports on what was done, and were opening played by the great civ players of yesteryear, those games are a huge help toward improving all aspects of play from openings, to trading, to strategies that can be applied at various points throughout games. The games I would recommend you read are
Sid Vicious and the Magnificent 7+1 (even if its the only one, its a terrific read as well)
Defiant Chinese Nationalists
Scouting Sid
these three games were the big ones that helped me. It's a bit trickier to find but Goz's (Goz6 iirc) 'Silence is Golden' game is also a terrific game to learn from.