I immediately went and settled on the gold mine to the left -- got River + Mountain + immediate lux (once Mining was researched). Scouted around and found both Ghengis and Alex (plus Sejong, but he was less of an immediate threat). Settled second city next to Natural Wonder, third to east on Marble, fourth to west on coast.
Saw a lot of Mongol units near my second city and was worried, so spent several turns building up enough of a force to defend it. Turns out Ghengis was only after Sidon. In fact, on turn 72...
I had Declarations of Friendship with Alex and Ghengis (plus Korea and I think Siam).
Turn 82 general status...
As you can see I was having some severe happiness issues and had to stop growth outside of my capital for a bit.
I managed to bribe Alex to get into it with Ghengis in order to keep him off my own back potentially (I felt safe while DoF was active but potentially worried when it expired -- I was directly in Alex's path).
Turn 100 report:
National College 13 turns out. Behind schedule but given how worried I was initially about Alex/Ghengis I felt it wasn't too bad. Of course, Alex decided to settle between my cities and cut them off. That may not have actually been too terrible overall, though -- it also gave him a clear route north without him feeling he had to go through my lands. Definitely messed up plans for expansion and resulted in western city not having enough territory, though.
Turn 151...
Continued to have Alex/Ghengis occupied with wars, which Siam then joined in against Ghengis as well.
Was basically forced into Order by Sejong lest I suffer major happiness issues -- I actually was first to pick I believe, but I saw where the wind was blowing. Siam went Freedom and Alex went Autocracy but managed to be friends Alex the whole game and at least Friendly with Siam.
Turn 200...
Turn 230...
About this time I realized Korea was like 10 techs ahead of everyone else (was signing research agreements with everyone). Managed to get Alex to go to war against him in the hopes of slowing him down, but didn't seem to help much and Sejong conquered some of Alex's city states.
I started building up a battleship force with a carrier with fighters (even went and settled a new city on oil on an island to the southeast for seven more oil) that wound up getting a few missile cruisers (rushed straight to Hubble and then Robots after Research Labs) but it was too late.
Turn 286...
Yeah...
I thought losing a cultural victory on turn 316 to the AI was nuts, now I've lost a 290 science victory.
Anyway, feel free to ask any questions you have about the game and I'll answer as best I can, may not remember every detail at this point. Do have a few saves I can load to check stuff out, though.
I definitely had a bad start and didn't leverage my science well enough mid-game either -- used to cargo food shipping my capital which I couldn't do here which hurt.