Unlike my competitors i went for Republic. My guess was that a large amount of cities and the gold bonus would more than offset the unit support cost. It seems that i was right, since the money paid for units never went past 60 gpt and in the later turns, when i started disbanding units to rush temples around, it even dropped to zero.
In 1075 BC the Egyptians completed the Pyramids in Thebes. For the wonder cascade effect Babylon built the Oracle next turn and Memphis switched to the Great Lighthouse, that was completed in 875 BC. That would make an interesting scenario: Babylon is the obvious first target, since controlling the western part is paramount to achieve a fast domination. From there units may be sent to take over America, Iroquois, France and the rest of the enemies in a clockwise pattern. Moreover, New York is the ideal location for a capital jump and once established the new core more units may be trained and tossed quickly into the battlefield.
But Egypt is an important target as well, to be secured as soon as possible. Given that 1) we're in Republic and 2) we aim at domination and 3) we still have a vast land to fill, then settlers, workers and population are important at least as military units. The growth bonus given by the Pyramids would be too much of an advantage to be ignored.
What is clear now is that things are far from being obvious. An important strategic choice was to be made soon, and it will influence the whole game. Where to go first? Babylon or Egypt?
My choice was: both of them

Here's how i dealt with it.
A stack of elite jags and horses is assembled at the gathering point. Once most of the roads will be built, it will be sent to strike at Babylon and Ur. Should one of the attack fail, or a city defect, fresh mounted units from the core will be quickly available for a second hit. Babylon is a culture monster, so in order to minimize the flip risk, the Iroquois will be drawn on the fight in hope they dispose quickly of the 3rd Babylonian city, Niniveh.
It is important to achieve at least a jaguar victory to start our golden age. Should we fail in it, we'll be in real trouble.
Once the primary target is secured we'll continue the offensive to New York. From there we'll take over Washington and the whole America. Iroquois and France will only have to wait for their turn.
To assimilate Egypt, we firstly upgrade to flails all the jaguar and swordsman units that are still in veteran status. Elite swordsmen will be kept as they are. Those units will form a second stack that will be shipped via galley chain in the dye colony to the north. From there, they will strike at Thebes, then capture Memphis and finally Heliopolis. Later in the game, the cities of Memphis and Heliopolis will provide useful basis to launch an offensive to England.
The drawback of this plan is the cost. Upgrading the jags and rushing the necessary galleys will cost us A LOT, that's why we need the golden age so much right now.
So we'll have a two-front war that will go on from the whole game. An army of fast units will secure the western part, then assimilate Iroquois and France, while a second army of slow but powerful units will take care of the smaller Egyptian and English part. Meanwhile, in the core the necessary workers and settlers will be trained to road the necessary tiles and claim the empty space.
I have written already a lot, so i will spare the details. There were some minors setback: first, the Iroquois weren't of any help in the capture of Babylon, so we had to sign a RoP with America and go to take over Niniveh by ourselves. Second, the city of Babylon flipped once, but the loss was small and it was recaptured immediately. Finally, a pair of serious SOURs (Strings Of Unlucky Rolls) costed us two failed attacks, one in Paris and one in the last Iroquois city, but fresh troops were quickly available and the captures were just delayed of one turn.
Apart from those minor glitches, everything went well. We also got the necessary leaders to jump the capital in New York and to rush Sun Tzu, and two more leaders that we used to rush the Great Library and the Great Wall, mainly for denial purposes. A fifth leader to rush the Hanging Gardens never came, so we failed to secure all the available wonders, but it's really of little importance. There was also a small war with Spain that netted us two spaniard cities and provided some useful extra tiles to achieve domination.
The military campaign started in 775 BC, and we've been in a constant state of war until 230 BC. At that point the game was essentially over, the temples i rushed in that turn and the 2 planned settlers would provide the necessary expansion to hit the domination limit without the need of any further offensive, but i went on just for fun.
The domination limit was hit in 130 BC, for a Firaxis score of 9829 and a Jason score of 12060. Here's the final minimap: