Wow, no one has written any spoilers for this game at all? Okay, just a brief one from me then...
Settle in place and plan up a settler factory with all the food we have here. The Persian pike shows up very early and parks itself on the isthmus, so for a long time I knew only the Aztecs and Persians, and even after I met the others, it wasn't until very late that I actually sent units through the Persian blockade (i.e. by force). Sparta went on the river RCP4 east of Athens in 2900b - this will be my 20k city, supported by all those juicy hills and grasslands, even if it doesn't quite reach a bonus food source.
Slingshot acheived and Republic installed in 1500bc after a 2 turn anarchy - obviously I had a reduced number of towns at this point. I reached the medieval in 775bc, getting Monotheism free, and at this point Sparta has still built only a temple! Its first wonder, Oracle, isn't done until 670bc. Sounds like a slow start for a 20k, I guess I didn't pump it up in size fiercely enough, but I was having trouble with barbs, and happiness, and not having enough workers. Anyway, Sparta gets Glib in 150bc to start the golden age (I already built Lighthouse over on the coast, just in order to get the GA going - otherwise I would be waiting for Smith or needing to capture something from the AI). But after this slow start, I still managed to get all the cultural wonders (i.e. more than 1cpt per 100 shields) except Gardens.
As for the AI, I started with the Aztecs in 190ad, using mainly horses, then finally headed west in 630ad, starting with the Persians. I carefully keep X-man alive in the middle of the huge mountain range, up until the point he can teach me his modern free tech. The Mayan campaign starts in 930ad, and they survive due to having settled the one tile isand. Similarly the Roman campaign goes unfinished because they have holdings beyond Gaul and I can't be bothered to go there until after I've done with the Celts.
By the time I attack the French and Celts, I can't really take much more territory without going over domination, so I abandon the old Aztec province, in order that I can keep the Pyramids (and Sun Tzu and Leonardo) in Entremont, and the French spices. Sparta finishes building culture in 1505ad, and then just cruises along at 151cpt, reaching
20k in 1700ad.
Cultural builds in Sparta...
1675bc temple (1022c)
0670bc Oracle (1672c)
0650bc library (1245c)
0550bc cathedral (1200c)
0150bc Great Library (2040c)
0090bc university (1324c)
0050bc colosseum (650c)
0230ad Shakespeare (2264c)
0320ad Forbidden Palace (518c)
0380ad Zeus (964c)
0580ad Michelangelo (1086c)
0700ad Copernicus (580c)
0800ad Newton (810c)
0860ad Bach (774c)
0920ad Darwin (369c)
1000ad Suffrage (460c)
1020ad Epic (452c) (not much leader luck this game)
1080ad Smith (321c)
1120ad Academy (103c)
1150ad Wall Street (200c)
1240ad UN (364c)
1290ad Internet + lab (328c + 164c)
1335ad SETI (219c)
1350ad Pentagon (70c)
1375ad Hoover (130c)
1385ad MASH (63c)
1415ad Longevity (171c)
1430ad Apollo (108c)
1455ad The Bomb (98c)
1460ad Palace (48c)
1485ad The Cure (129c) (in 5 turns!

Fully mined and improved, Sparta hit
201spt, and it always had good luck with pollution)
1490ad CIA (42c)
1505ad Star Wars (39c)
1700ad Victory (20027c total). 4716 Firaxis points makes only 8933 Jasons.