I first bought Civ3 shortly after Christmas of 2001 and started up my first game with virtually all the default settings: standard map size, configuration, climate, etc. The civ was the Romans, since they are my favorite historical civ, and the difficulty was Chieftan. Since I had never played the game before, I thought I'd run it on the easiest difficulty so I could teach myself how to play without getting creamed. I suppose I should also mention this was the original, unpatched version of Civ3, which is not much like the current version at ALL.
I can't say too much about this game because I unfortunately no longer have a savegame from it. I accidently saved over it when playing a later game, so I can't provide any maps, or pictures, or look at my early follies in detail. But I can narrate what went on in the game. I started in the middle of a bunch of grassland tiles, with a few hills nearby. It was a decent starting location, but not a great one. Like most new players, my biggest mistake was not building enough cities; I'm sure if I could watch a replay of that game now my expansion would look painfully slow. The Aztecs ended up starting about 3 city-spaces to my south, and I fought an early war against them with archers. Given the crippling disadvantages that the AI works under on Chieftan difficulty, it's not surprising that I was able to win, though my horribly bad strategy should have cost me here. But you can get away with just about anything on Cheiftan, so I was able to get a couple of Aztec cities, which was good because I had only built 2 of my own in the first 100 turns!
As it turned out, the French were my neighbors to the east. The Aztecs were dead by 1000BC, and there was a large jungle south of them. Past that were the Egyptians, Iroquois, Americans, and the Babylonians. The English started out on an island in the middle of nowhere and played no role in the game at all; the map was virtually a pangea though I had selected continents. I out-researched the AI in terms of tech (of course) and eventually attacked France with knights and legions. I should mention as well that I never conducted any diplomacy in this game at all. I just saw the AI civs as opponents to run over. I guess I was still stuck in my Civ1 mentality, where that was more or less true. I would improve in later games though, as you can see on my site.
My war against France lasted a very long time. I didn't commit enough forces to the task, thinking I could get by with only a few knights, and I consequently failed to keep producing more to replace those that died. I think part of this was due to my previous experience with Civ1, where I would reload when combat results didn't go my way. (Hey, I was only 11 years old at the time :) But regardless, I didn't prepare fully enough for war, and as a result the fighting dragged out for a VERY long time. Inevitably though (on Cheiftan) I gained more and more of an advantage over France and ultimately conquered them.
By this time I was by far the most powerful nation in the world. I had a good chunk of territory, about 1/3 of the total land area, and (completely by accident) a good Forbidden Palace placement in former Azteca. I didn't understand what the FP did, and had built it there randomly. Nice! I also automated almost all the workers in this game, though I started to unautomate them later as they prioritized cutting down jungle over building rails in my core cities, and I could see even then that that was just silly.
I went into a democracy at some point and tried to research up to tanks. But this was the original version of Civ3, and tech moved really slowly, so I decided to fight wars before tanks arrived (since they were taking so long). I was of course an age ahead of the other civs in tech (it was Chieftan), so it was infantry and cavs against pikes and muskets. I can't believe I initially thought that infantry were better than cavalry on offense since both had 6 attack and infantry had much higher defense! But even in the course of this game I discovered that 3-move units are much stronger than their numbers would otherwise indicate.
Despite doing a ton of ridiculously stupid things in this game, I still won a domination victory in 1952AD. I had killed Azteca, France, Egypt, America, and Babylon at that point and was surprised to see the game was over. I was bored with the game though, so I wasn't disappointed or anything like that. I still had not reached tanks yet on the tech tree. On the whole, this game was a great experience for me. It taught me many of the basics of the game in a pressure-less environment. But I knew that it would be a waste to stay at Chieftan level any longer than for one introductory game, so my next one was to be played on Warlord, where I hoped to get more of a challenge.