OK. So this is both the first time I have ever tried GOTM and the Monarch difficulty, so I won't be expecting much of my end result.
For me, I got to a surprisingly slow start, considering the very early UU of the Aztecs. However, I didn't want the GA to start so early so I restricted my early warfare to the use of archers, and kept JWs out the back for a future GA trigger once I could switch to Republic without compunction.
The Persians founded their second city four tiles away from the borders of Tenochtitlan, so I sent a stack of archers to try and apply some pressure, and perhaps burn the settlement to make room for my own expansion. Unfortunately, there was only 2 in the stack, I was utterly desperate and lost both of them. I returned later with four, then marched further towards Persia with eight as my cities came up (I built barracks first, then started pumping out archers if there was already a JW defending the city).
When I sued for peace with Persia (though they still had quite a bit of their empire left at that point), I got quite a few techs off them and turned towards Russia with a stack of 14 archers and 4 spearmen (again, trying to avoid the uncomfortably early GA). I took Moscow and two other cities, sued for peace and started cranking out JWs (for upgrade to swordsmen) and chariots (for later upgrade to knights).
I switched to Monarchy as soon as I got the tech and my economy boomed. I imported Iron from Russia (since I hadn't yet conquered their ore fields) and upgraded the bulk of my JW horde into swordsmen. Using them, I went to war with Egypt, captured Thebes and gained the Great Lighthouse (as well as knocking them out of the race for the Great Library). Cleo begged for peace after that.
The Romans had become quite an annoyance, having wiped out China really quickly and controlling their entire island. On two occasions they demanded tribute, declaring war when I refused to give in to them. One such time, they allied the Zulu against me (though no battle was fought in that war).
In the middle ages, I completed my conquest of Persia. All that remained of them was Tarsus, a city established northwest of Zululand which was later wiped out by the Zulu.
Next I turned towards Russia, again leaving them with nothing more than a couple of backwater settlements of theirs near Zululand's northern border. Towards the end of that war, I sent my stack of jag. warriors into the mountains near Tenochtitlan (since they sent a stack of archers and swordsmen that way), switched to Republic and let the Russians try attacking my JWs. Needless to say, it fired up my golden age. I immediately sued for peace and built up more horsemen, markets and cathedrals in the newly conquered Persian and Russian cities, and Leonardo's Workshop (unfortunately, the Iroquois beat me to Sistine Chapel).
I am currently assembling an invasion force of knights and pikemen and a huge fleet to invade the Romans and perhaps redeem the honour they robbed me of. Also, I plan on gaining Copernicus' Observatory, which Rome built very quickly (having been beaten to Sistine Chapel as well, they immediately switched to it). Perhaps Rome will be my FP location, and I could try and get Newton's University.
I haven't gone any further yet, as I am still assembling my invasion force. My goal will be to seize their capital as early as possible, and take one of their ports so as to be able to quickly prepare new arrivals for battle, supply the newly conquered territories with luxuries from the mainland, and supply the mainland with some of that sweet Roman wine. And all hopes are on getting a leader in this upcoming war so as to be able to make the FP possibly very quickly.