An interesting game because of the geography (very long in the E-W direction). Frequently I start military operations once can build crusaders, build lots of them, and try to conquer lots of AI cities until I discover democracy at which time my emphasis often shifts to infrastrucure and science.
This time I went for a very early republic (much earlier than I usually do), even without HG and Mike, established an SSC that quickly reached size 8 and 12 soon after that, and then started churning out caravans and caravels. Since the map was big and the AI far away I left most of my cities undefended and concentrated on trade using large shipchains. The only exception was the Aztecs, they were very weak (4 cities and little cash) when I met them so I bought/subverted all of their cities (the senate signed a cease fire so I subverted some cities). Once they sneak attacked I captured Tenochtitlan using just a single crusader and they were history.
I also established a colony in the westernmsot part of the large island east of the starting island. Further east was the Roman empire; I established a border at a nice choke point but didn't fire a single shot at them for a long time but used them as a trading partner. Once I discovered railroad I wanted to shorten my shipchain by capturing a few Roman cities east of my colony. At this time my technology was advancing very fast so before I had finished preparing this I discovered espionage and the Roman cities turned out to be so cheap I didn't fire a single shot at them but bought the five cities I wanted and established a new chokepoint. Now I was able to greatly increase my trade with the Carthaginians and especially the Zulus. I mainly expanded towards the east and the Carthaginians were east of the Romans and the Zulus east of the Carthaginians. This resulted in huge delivery bonuses so I soon discovered automobile and built lots of superhighways. Once this happened I usually acquired two techs per turn until I started researching future techs at which point I raised the luxury and tax rates a bit. All of this happened so fast I sometimes didn't have time to build some of the wonders I wanted until 20-30 turns after discovering the relevant tech (examples: AS, WS and Hoover).
I was too busy advancing to build any military units until I could build armor, howitzers, stealth fighters and paratroopers - I didn't fire a single shot at the Romans until I had built one howitzer and one armor. I never built a single dragoon or cavalry (those I have are barbs I bribed). I also prioritized automobile ahead of tactics. Usually I'm interested in tactics because I love having a big military and I want Leo to upgrade it but this time I had only a few crusaders so the fact that Leo expires with automobile was irrelevant.
Now the Romans are history and I'm attacking the Carthaginians, Zulus and Vikings (and soon the Persians too) with howitzers, stealth fighters, battleships, armor, spies, engineers and paratroopers (my army is still small but very hi-tech and rapidly growing). Their cities are defended by warriors (!), phalanxes and musketeers

. In theory, one stealth fighter and one paratrooper could easily conquer the world - my technological advantage is overwhelming. I could have won earlier (I'm not finished) and gotten a better GOTM score but this is fun.
Status in 1555 AD:
59 cities, 57,260,000 people. Researching future tech 8. Only 4 gold (!). 52 engineers, 1 warrior (!), 1 phalanx, 8 musketeers, 25 riflemen, 2 paratroopers, 3 elephants, 7 crusaders, 4 knights, 3 cavalries, 4 armors, 1 catapult, 3 howitzers, 4 stealth fighters (many more under construction), 1 battleship, 30 transports, 11 spies, 9 freight. All wonders except pyramids, HG, Lighthouse, GL, Oracle, GW, Sun Tzu and KRC.
Zulus: 9 cities, researching NONE (just discovered gunpowder), 1676 gold.
Vikings: 18 cities, researching democracy, 1408 gold.
Persians: 12 cities, researching steam engine, 1970 gold.
Carthaginians: 11 cities, researching magnetism, 434 gold.