Frist spoiler here :
http://forums.civfanatics.com/showthread.php?p=4210689&posted=1#post4210689
I'm going for cultural, picking up from first spoiler, c. 600AD, I have my three cultural cities set up, and three peripheral cities for spreading religion and building military if I have to. I've just ended an early war against Isabella that she started.
I grabbed the Pyramids, Parthenon, Stonehenge, and the Hinduist shrine, all in Mecca. Victoria and Caesar have converted to Hinduism. I didn't attempt the Oracle, as my tech path was too messy.
Partly because of all the jungle, all my cities need a lot of work. Improving my cities and keeping good relations with my neigbours is my priority. I abandon my religion as two neighbours are threatening to wage war on my civilization.
c. 935AD: Chichen Itza is completed in Mecca that has now pretty much become my wonder city and great person farm. This is my first attempt at a cultural win, and I have little experience in generating great people. Mecca is a mess with all the wonders, and I get great prophets where I'd rather have scientists for academies. Or great artists. Still, great people are never lost, I use whatever I get to improve my other cultural cities and my economy. Other civs keep switching positions on the score, most are rather backwards, and I'm able to trade techs to stay ahead. My workers are busy minging, setting cottages, farms, linking resources, and chopping the jungle tiles. I shot for Music for the free artist, and intend to build the Great Library for free scientists. Victoria is not far behind in tech however. The Greeks are bringing the Incan civ down.
c. 965AD. Warwick revolts and joins my empire. Shouldn't have settled so close to my civilization. Another city that needs a lot of work.
c. 1000AD. I begin work on the Great Library in Mecca, and Notre Dame in my second cultural city Medina. Unfortunately, I have no great engineer at hand.
c. 1070 AD. I can now switch to bureaucracy. Rather late.
c. 1172 AD. The Japanese beat me to the Great Library. I had a great engineer a few turns before, but decided to save him as I was only a few turns from completion. Oops. I'll build the Great Collossus.
c. 1202 AD. I found Islam in Damascus, my third cultural city. I need religions, and other civs didn't spread much of anything to me. I now have hinduism and islam I founded, and Taoism I got from Warwick when it revolted and joined my civ.
c. 1250 AD. Notre Dame is completed in Medina.
c. 1262 AD. I have good relations with everyone, especially Isabella despite our early war (but then she started it). The Japanese declare war on the English, which is a good thing for me, while other civs are waging war, I'm building my techs.
c. 1280 AD. I complete the Collosus in Mecca. Next is the Sistine Chapel, though I doubt I'll complete that.
c. 1346 AD. Caesar declares war on the English too. The Japanese are already at war against the english, and with the help of Caesar, I'm afraid they capture english cities and grow stronger.
c. 1352 AD. Alexander beats me to the Sistine Chapel. I go for the Spiral Minaret.
c. 1358 AD. Alexander seems to have a large territory thanks to the Inca but rather backward in techs. I have decent relations with the Japanese and decides to bring another civ in the war against them, I can afford the -1. I bribe Alexander into war against the japanese with a couple techs. That will keep them all busy.
c. 1376 AD. Mecca completes the Spiral Minaret.
c. 1382 AD. Tokugawa, now busy with Alexander, makes peace with Victoria. The English and Rome are still at war.
c. 1412 AD. Victoria and Caesar make peace.
c. 1424 AD. Isabella, who's rather backward, joins the fun and declares war on Tokugawa.
c. 1508 AD. Versailles is completed in my third cultural city Damascus. That'll gain me a few coins.
c. 1529 AD. I discover liberalism! I pick astronomy as a free tech. I'm way ahead in tech at that time. I should have switched to culture at that point, but submitting my game was not on my mind yet, so I keep researching for a while and decide to make the switch to culture when I discover democracy and complete the Statue of Liberty (a second free specialist in all cities, who can resist that ?

).
c. 1550 AD. Another civ (I think Isabella) asks me to declare war on Tokugawa, already largely busy with Alexander and Isabella. No risk for me there, I go for it, though I don't intend to make anything of it, it just made good sense diplomacy wise.
c. 1553 AD. Ghuzz revolts and joins my empire. Sorry Caesar.
c. 1568 AD. Alexander makes peace with Tokugawa.
c. 1589 AD. I make peace with Tokugawa too, no sense for me to stay at war if I'm not moving a single unit.
c. 1592 AD. Isabella makes peace with Tokugawa as well. Everyone is at peace now. Wars kept all the other civs in check while I was free to develop my empire, I'm well ahead in score now.
c. 1634 AD. Peace was short, Caesae declares war on Victoria.
c. 1664 AD. Alexander declares war on Tokugawa again. This time I'm not involved. Victoria makes peace with Caesar.
c. 1697 AD. I discover Democracy and instantly build the Statue of Liberty with two great engineers I had saved. My cities are well developped (though Medina, my second cultural city hasn't grown that much), I make the switch to full culture. I have plenty of techs to trade for many turns to come. Time to build missing religious buildings and spread available religions between my cities. I have Hinduism and Islam that I've founded and Taoism and Confuscianism from cities that joined my empire.
c. 1700. Tokugawa signs peace with Alexander after losing one city. Alexander is doing fine on the score thanks to his large territory but a little backward in techs. Tokugawa, Caesar and Victoria are doing fine, but apart from Victoria, are also way behind in techs. Isabella is second to last with a decent territory but a lot of missing techs.
c. 1712 AD. Isabella, always eager for another war of religion picks the poor Incan with two cities left.
c. 1744 AD. Isabella capture the last of the Incan cities. My borders keep expanding, and chances are that city will end up in my empire soon, as well as a small english city to the north left with only two tiles. I'm busy spreading religions for buildings and also on foreign soil for money with my hinduist shrine.
c. 1800 AD. Isabella declares war on Tokugawa. She just won't let go. The former Incan city now a Spanish possession is left with just its central city tile and will probably revolt soon. The english city is holding. In 1842, Isabella makes peace with Tokugawa.
c. 1827 AD. Aryan revolts and joins my empire, as expected. Thanks Isabella! Around that time, I'm spreading Judaism around, which spread to one of my cities.
c. 1834. More warring, Caesar goes for Alexander this time and quickly loses its two cities part of the former incan empire and cornered by the Greek empire. A few turns later, Caesar will capture then lose, then recapture, then lose again one of the Greek Cities.
c. 1842. I get another great prophet and complete the Islamic shrine, more money and a shrine can't hurt my economy and culture.
c. 1847. Tokugawa declares war on Alexander and immediately captures a city. Alexander soon makes peace with Caesar.
c. 1875. At last, all my cities reach legendary status on a "culture bomb". Despite quitting research some 180 years before, I'm still in a good position tech wise. Amazingly enough, the small english city never revolted, yet it had been left with just one tile and well within my own territory for quite some time.
Final score: 12,620 on contender. Had I planned to submit my game, I probably would have switched to full culture much earlier, but oh well, I'm happy with my first GOTM and first cultural victory. That was fun.
Major mistakes include my early tech path (quite messy, didn't go for bronze working despite intending to chop my first workers and settlers), the razing of Badgad, my fourth city, by Barbarians caused by moving my axeman defender out of town for no reason, getting beat to the Great Library while I had a great engineer in stock, and not making enough workers early in the game with all that jungle.
Also, making my first city my great people farm as well as a my wonder factory meant I had little control on what great people I got (and I failed to grow the city fast enough for a great person farm as well). Less great prophets, more early scientists for academies, more great artists would have helped.
On the positive side, I kept all the civs in check through diplomacy (though that was made easy with picking no state religion), and was in control of the game all the way through (but then, it's only on Prince difficulty).