The early research path was by FAR the most critical decisions to make in this game. We had the continent to ourselves, so it really didn't hurt anyone to grow and expand a bit slower.
I researched Pottery - Writing - Masonry (for the Pyramids) - Literature - Map Making - Ceremonial Burial - Code of Laws - Philosophy - Republic, and revolted.
My second city started on the Pyramids at the moment of its founding, and finished them in 750 BC. Built the Great Lighthouse, found Egypt in 10 BC, traded for their map, and had contact with everyone by 150 AD. Built the Great Library in 210 AD which leapt us into the Middle Ages, and triggered the Golden Age which I didn't realize it would.
I whipped a ton of libraries and temples, content to ignore the 10 AD population goal. The Forbidden Palace finished in 270 AD, three cities south of the capital. There just wasn't really any better location for it - maybe on the island, but that would've taken twice as long to finish. I colonized the large western and small eastern islands, plus the two tiny islands to the northeast.
Researched up the Education side of the Middle Ages tree, getting Universities built as soon as possible, and revolting into Democracy. Every tech from Theology until endgame took the minimum 4 turns to research.
Nearly swept the wonder picture, getting the Hanging Gardens, every medieval wonder except Sun Tzu's, Leonardo's, and Newton's, and of course all Industrial and later wonders.
Egypt declared war halfway through the Industrial Age, so I popped over with tanks. I.... got stupid in this war. I kept sending tanks out from the main stack to chase riflemen that were sitting around. They killed them, but then got swarmed by a half-dozen infantry and killed. I only razed three cities (including two great wonders - first time I ever did that) before running out of tanks and stopping.
Built Longevity in 1380 AD, getting a big boost towards 1500 AD population.
Game goal summary:
10 AD Population: 2,979,000
1500 AD Population: 137,145,008
Modern Age: 1320 AD
Civ-Wide Cultural Victory: well, read the conclusion.