Well, this is the second GOTM that I've played and the first I'm going to do a spoiler for. After reading the plays of others here I felt moved to write my own and see if I match up, being kind of new to Civilization 3. If it seems unprofessional just bear with me.
Difficulty Class - Conquest
Where to start? Well, I'll start by saying that it turns out that my route in the early game dirastically differs from most here. During my opening turns I bumped into a Chinese warrior and settler that were still quite close to their city. My warrior was just in sight of their boarder. I don't want to tell the whole story in my introduction, but to be brief I eliminated the Chinese threat entirely. I'm inclined to believe that they were a driving force behind the rapid technology advancments in this game. At the point in time I reached my middle ages, the most advanced civilization, the Ottomans, were 5 techs ahead of me, with only 4 of those being from the middle ages. It is 30 B.C. Most others here were entering the middle ages, no doubt slightly behind in the race, around 1000 B.C. This is a rather interesting find, as in your games the leader should have 2, 3, maybe even 4 more techs then that by this time. This knowledge makes me optimistic that I'll be able to pull ahead from an other wise slow start.
The Opening Game
Like most here, I moved two spaces north of our initial position. Athens was founded along the shores of what will be dubbed the Athens River in 3900 B.C. I sent one hoplite through the mountains in a westward direction to explore and fortified the other in Athens. A few turns later in 3650 B.C. I sent my first warrior exploring to the north along the Athens River. My exploring hoplite quickly came to the end of the mountain chain and continued west to see how far out the jungle went. In doing so he stumbled upon the Indian civilization whose city was located southwest of Athens. There was a quick exchange of knowledge before my hoplite headed north.
War With China
To the north my warrior had encountered a Chinese settler with a warrior escort. Contact was made and knowledge was exchanged. Then I got to thinking, "I decided at the beginning that I felt like getting a conquest victory. This would be as good a time as any to start." Indeed, it was a strategic decision. If my warrior could manage to kill that escort and capture the settler not only would it net me two free slaves but it would cause China to stop focusing on expansion and technology. The downside would be that they'd focus on taking over my cities. But I had an advantage. First, they had no clue where Athens was. Second, even if they did find Athens they'd still have to produce troops with a fledgling city and run them down there. Third, they'd have to get through the defenses, which were now two hoplites. If things went sour I could always just fend off their attacks with hoplites guarding workers and escorting settlers. If I played my cards right the war could work out for me whether I won or 'lost'. As it was, I won. I defeated the enemy warrior and directed my prize toward wines south of Athens (my starting workers were busy digging a path through the forests to the north to the site of what would be my second city). I directed my exploring hoplite to the north in the general direction of the chinese city which had come into view when my warrior moved into the position the settler had been in.
Sparta was founded in 2750 B.C. and set about producing an archer. Giving me the Warrior Code would be China's undoing. Meanwhile, for better or worse, my hoplite to the west had attacked and defeated a Chinese warrior, triggering a Golden Age. A rather shocking amount of warriors, archers, and spearmen poured out of the fog and into sight of my warrior and slaves. I was starting to wonder whether I could possibly take on all those units. I probably wouldn't have been able to, but I had both the money to support a relativly large army and the production to churn it out due to fully improved tiles around Athens and the woodland game outside Sparta. One hoplite was already in Sparta and two were in Athens. They were soon joined by an archer produced by each city. The first died in his first fight, redlining a fortified warrior outside Sparta. The second took out that warrior as well as two spearmen and another warrior that had moved (but apparently not fortified, at least not the first spearman) within striking distance of Sparta. This archer, followed by another fresh from Athens, struck out north to take out two archers headed toward Sparta. With my two archers on a mountain and China's two on a grassland tile north of the mountain, they didn't have a chance. One of my archers attacked and killed flawlessly, and the second was taken down to yellow by the remaining archers following counterattack.
By this time my western hoplite had uncovered the tiles surrounding Beijing. It was apparently their only city, only size 1, and they apparently had no other units wandering around as they had no contacts other then me. This being the case, I sued for peace and got The Wheel and 58 gold out of it. I closed the diplomacy screen, re-opened it, and declaired war on them again. As far as I know this ruins your reputation (especially since I still had that hoplite in their territory). But if they don't have contact with anyone else, no one else has to know. So I decided to devote my resources to building two more archers and an attempt at taking Beijing. Meanwhile, my hoplite pillaged a mined cattle with road access, a mined wild game with road access, and I believe a shield grassland tile that was mined and had road access. A very nice starting position. A Chinese archer left the city to defeat a barbarian to the north, putting him in range of my hoplite. My hoplite attacked and scored another victory for Greece. This was fortunate as then there were only two spearment in the city as I would learn. With 4 archers at his doorstep, Mao made a bid for peace. He was rejected as he has nothing to offer and my archers attacked. Two died and the last one made it in, capturing Beijing for me in 1870 B.C. A turn before I had founded my third city, Thermopylae, making Beijing my fourth.
This did not eliminate China from the game though. I figured that they might just still have troops walking around. There would have been little I could do about that unless they came back. Howeve I initiated diplomacy with them a few turns later and found that there was a city under their 'Cities' heading: Canton. This was not good. This meant that they still had two cities somewhere. I demanded Canton in a peace agreement and they conceded. The city was south of the jungle to the south of us. Due to the corruption and the barbarian attacks that I realized would be regular, I soon abandoned the city.
With the Chinese basically defeated, or at least driven out of my potential land for expansion, I decided to bring my early campaigns to a close and focus on expansion peaceably.
The Era of Expansion
It was now 1675 B.C. I had found horses to the south of Beijing and was making preparations to send a settler there to claim it. My fifth city claimed the dyes between Sparta and Beijing. At about this time the Indians demand 21 gold from me. Not being ready to get in a fight with the swordsmen I suspect they now have, I decide it would be best to humor them. It was at this time that I also started planning out how I'd catch up in the technology race. I had fallen a bit behind due to my lack of expansion and apathy toward diligent tech trading earlier. I believe I was three or four techs behind the most advanced civ I knew of (probably tied for the most advanced, in retrospect, as they were constantly later when I had more contacts to compair them to) which was India. I had also completely abandon exploration during my campaign and now it seemed as though boarders had filled up all the open spaces, making exploration difficult and effective tech trading impossible as a result. I decided that building up my own economy and mass producing settlers would be wiser then taking any time to build units to explore.
Mass produce I did. I honed in on claiming and working land and as a result built 12 towns spread from the jungles in the south to the two silks on the peninsula to the north and from the eastern shores to the desert to the west. They're fairly well developed at this time, this time being 30 B.C. They have abnormally low populations for cities of this time and there's still a bit more forest then I'd like for this terrain, but about 70% of the tiles that are being worked are mined/irrigated and have road access. This percentage is climbing fairly rapidly. I've had a few set backs in building due to those damned barbarians, but I'm recovering well enough. All other factors of my civilization are a little below par, but they're improving steadily.
Resources
I have access to Iron, Horses, Dyes, Wines, Furs, and Silks. I have access to two or more of every luxury resource and can trade them for techs and military alliances in order to keep the other civs powers in check (at least I hope. I'm not sure with how I double crossed the Chinese) or I can give them away to placate other civilizations and get better prices on techs. It looks like I might be forced to pay gold up front, so I'll need those good prices. I think I have a large enough territory to have a reasonable chance of saltpeter appearing within my boarders. It looks as though it'll be near Beijing if it's anywhere. If it isn't, it'll be in Indias territory. That I am quite sure of. I'll have to take them down quick if that's the case. I'll have to get Gunpowder quick so I can actually check on that.
City Improvements
I'm lacking in this area. I'd like to get a temple, library, and marketplace in every city in a reasonable amount of time, but that's going to be a rather large undertaking. Especially since Athens just happens to be in a virtual corner! Half of my cities are simply a morass of corruption, although I'm still in despotism. I'll soon have monarchy though, so I hope that improves things a bit. If it doesn't improve things, add Courthouses to that list. I don't particularly feel like becoming a republic with the wars to come, even with the unit support it offers.
As far as gold per turn goes, that's coming along suprisingly well. With some marketplaces I hope to surpass 20gpt soon.
Military
I have about 12 hoplites and 10ish swordsmen right now. Soon to have more swordsmen and probably more hoplites. As soon as possible I plan on upgrading these to Persian Mercenaries. These are the units I intend to fight the upcoming wars with. I have to juggle this production with the production of civic buildings. This is going to be the toughest balance if I want to raise an army to take out my neighbors right now.
Technology
I'm five techs behind the Ottomans and probably the Indians right now and two to four techs behind everyone else. Certainly not a hopeless situation, but it does mean that I need to scramble to get Gunpowder. I'm considering alternate methods to getting ahead fast, as opposed to creeping ahead in research myself with a couple bought here and there.
Those Damned Barbarians
This map is rife with barbarians. I didn't have too much difficulty with them untill 800 B.C. There were TWO massive barbarian uprisings in the same turn. Within a couple turns both were heading not for the weak Chinese and Egyptian cities that were closer to them, but to my cities. It turned out that one uprising took place in the west and one in the southeast. Both were composed of 16 horsemen. I got very lucky in the southeast, where a hoplite killed 14 of them, but the west was not so lucky. All 16 hammered the single hoplite and archer in Beijing. After about 11 failed attempts, a horseman finally broke through my defenses and promptly destroyed the temple I'd just spent 30 turns making. It had been there ONE turn, and then it was destroyed. I sobbed quietly as the other horsemen walked off with my hard earned gold. Between these barbarians and the Indian, Ottoman, and Arab barbarians, I couldn't keep gold in my pockets to buy techs. All three countries demanded between 20 and 30 gold. The money taken by barbarians and other civs would have been enough to buy another tech. These were certainly a setback for me.