Here is my pre-game strategy for Civ3. Following these four major steps (Ancient, Middle, Renaissance, Industrial) will require great precision, patience, and planning but all will pay off in the end.
In the Ancient Era acquire some strong allies. These allies will be there to bail you out in case of a war (which you should try to avoid at this point). They will also be willing to trade with you, which means you will be able to get valuable resources, undiscovered techs, money, etc... Now try not to stick out like a sore thumb in this era either. What I mean by this is don't be too militariastic, so culturally focused that you become too weak in the military front, don't become too large in size, etc... Basically just try to stay well rounded in all areas. As your nation continues to grow make sure you keep your cities close together. Doing this will make it easier for defence, which will be very important. Also, IMO it will pay off in the long run as well. Make sure you don't feel afraid to venture out and explore. Only use colonies at this point in the game when completely neccesary. Following these steps in the Ancient era will give you an edge for the rest of the game.
This is the time to now invest in culture and expansion the most. By now most Civs live in their own distinct areas, with each one having various amounts of land. Getting a fairly large chunk of land now will give you an edge throughout the game. Now your nation can't be so large that you are incapable of having a balanced Civ. Remember that the key for now is staying pretty well balanced. Even though, you will be interested in culture and expansion at this point. Jump starting the culture will make many resources available to you without having to use a colony. If you are to use a colony in this age again use it wisely. For a worker might be more valuable than a resource at this point. Continue having a solid enough defence that you will be well prepared for an attack. A tip for defending is to build many fortresses around your borders. In the fortresses try to make every other one contain an offensive unit inside. The offensive unit will give you the oppurtuniy to attack the enemy when they approach your borders. Only have every other fortress contain an offensive unit and all the rest contain defensive because remember you are still on the defensive. In your cities try to primarily have the best defensive units availabe to you. Plus have a sufficient amount of cheap, fast units laying around.
Renaissance Age -
Follow the definition of renaissance. For those of you who don't know what the simple definition is - rebirth. What does that mean? Well, get real interested in the arts and science first off. Continue to invest more into culture, but even more so into science. Now is the time to get a huge lead in science or at least be one of the top of the line science Civs. By now your culture should be pretty good, so investing more into it will make it great. Continue your defensive approach, but don't let other Civs request absurd things out of you just so you can stay at peace. Start to lay down the law the a tiny bit. Other Civs need to know that you are a Civ to be reckoned with.
Industrail Age -
It's time to hit the weight room so to speak. You've created your weight room (culture, expansion, science) now use it (military). Since you have probably irritated other Civs by not bowing to their wants recently you need to protect yourself. Wait, not only do you need to protect yourself you need to have the capabilities of attacking in fierce measures. Although, this doesn't mean that you don't continue to upgrade your weight room, just start to use it a lot more.
Modern Age -
Continuing on my previous metaphor, flex your muscle and make sure other Civs see it. You can interpret this however you want in game terms; for I am leaving the rest up to you. Good luck and have fun.