Soon after founding Damascus, the early foundation of what will later be called the "Party Society" is laid:
The Partenon provided me with an increased birth rate for great people, and produced 2 great artist points as well, which (together with my philosophical bonus) translated into my first +5 great person points (GPP) per turn. Mecca would be my city specialised on breeding great artists, and this was only the beginning...
Now that I had three cities, I would love Damascus to become a holy city as well. Having three religions would be optimal, as I had full control over them and could easily spread them into my cities. This would allow me to build three temples per city, and (more importantly) one cathedral (+50% culture output!) per faith as well! So I started to research Theology next, although it would take a long time to finish.
Meanwhile, I built a temple in Medina, which allowed me to convert one citizen into a priest specialist.
This generated 7 GPPs per turn and would produce a great prophet in 15 turns, which I would use to construct the Temple of Salomon, the Jewish shrine. The great prophet would raise the price for my great artists, but I felt it was worth it, as I planned to convert as many AIs to Judaism as possible for diplomatic purposes, and the shrine would be my main source of income. The culture it would produce won't hurt either!
For the purpose of converting the AIs to Judaism, I started to build Jewish missionaries out of Medina. That delayed building culture, but it would be a very good long-term investment, as staying out of wars by virtue of good relations to my neighbours will be the reward. Frederick and Victoria were Jewish already, so I planned to convert my third next neigbour, Louis XIV, next. Unfortunately he cancelled our open borders agreement on the same turn my first missionary was completed. Washington then approached me and asked me to cancel my open borders deal with Mao, but I declined. Mao had converted to confucianism, so our relations were getting worse already, but we had still open borders - and I wanted to use this to spread so much Judaism to his lands that he would convert! I started with Shanghai.
Note how I used my missionaries for scouting purposes, because since my scouting warriors had been killed by barbarians millennia ago, I hadn't had the time to build more scouts...
Judaism spread to Damascus on its own, which saved me a missionary. I used another missionary to spread it to Beijing, and bingo! In 250BC, Mao converted to Judaism! That was faster than I had expected.
During the same year, the great prophet emerged from Medina, and constructed the Temple of Salomon there as planned. My income increased immediately. Then I removed the priest specialist from Medina, not needing more prophets and not wanting to raise the great artist cost unnecessarily.
All my plans regarding religions seemed to work nicely, except one. In 325BC, Washington founded and converted to Christianity, seven turn before I would have researched Theology! One chance to make a third holy city passed, two left (Islam, Taoism). I went for Divine Right (Islam) next - but failed to get that as well! Both Islam and Taoism would be founded later in 760AD, two turns before I had the chance. Argh! I'm sure I had done some moves before or passed a chance of micromanaging things which now had cost me these two turns...and so I failed to get three holy cities. Hopefully that was no bad omen!
Remember my goal of reaching a cultural victory?
Not the best of starts it seems. *cough* But bear in mind that I faced creative civilizations, and that I had to make some long-term preparations which would pay back later, like spreading Judaism. I will overtake them, whoever that unknown civilization on the top spot is, I promise!
In 50AD, Louis declared war on Frederick! Louis was still cautious towards me and would not sign another open borders deal, so this war was fine with me: Keep him busy elsewhere! Some turns later, I contacted the missing civ (Egypt), and discovered alphabet and was finally able to do some trades to bring me on par with techs.
Phew, I wanted to get experience with diplomacy and trading, and here I got some! I had been far behind in tech, but after that round of trading, including trades where I brokered newly acquired techs (Monarchy and Meditation) immediately away to another AI for even more techs, I was on par with the rest of the world. Note how it's already AD times, and yet it's only now that I manage to get worker techs like Mining, Bronze Working, or Pottery! I simply didn't have the time to research them myself, and I find it ironic considering how many people think it is the best strategy always to go for bronze working first to be able to chop forests to rush things... No, the best strategy is to adapt your decisions to your long-term plans and the current situation, and in this case this involved ignoring Bronze Working in favor of other things.
Also note that even with my slow research (three cities only, and going for theology first), I was still first to discover Alphabet! I had seen this several times now, that the AIs neglected to research Alphabet for a long time; it nearly always makes a worthy research goal, as it will give you lots of trading opportunities. It's highly questionably in my view that the AIs don't go for Alphabet sooner themselves, but maybe some leaders do this, or I just got (un)lucky in my games - I need more data to really make this assessment, but it's something to keep an eye on.
After these trading rounds, I adopted Hereditary Rule and Slavery (though I never whipped anything during the game). While Medina had been busy producing missionaries, Mecca had built another crucial wonder for my strategy, the Sistine Chapel!
This wonder had been another reason why I went for Theology so early: Two additional great artist points! Ten culture per turn! And two culture per turn per specialist in all cities! Especially that last bonus would be very powerful later on, when I would hire a lot of artists in my three cities. Good thing I had marble available to build this; for this kind of strategy, I really prefer having access to marble over stone!