Hi--I just got done doing some theorietical research in preparation for GOTM7 (level: Deity--so I'm a bit scared). On all the levels, however, it's advantageous to expand your civilization as fast as possible, so you can snatch up valuable land before your rivals do.
This advice is most relevant to someone playing on Deity, though it will be useful for other contexts too.
I assume that there are at least three grass-with-shield slots inside your capital after the first border expansion, and at least one is available before.
First you set a citizen to work the grassland with shield while making a warrior. Then you take your first worker and assign him to dig a MINE on that spot. Meanwhile, the warrior pops out. He's not needed in the city yet, and has about 15 turns to explore the neighborhood before he needs to come back and prevent disorder at pop=3. The second warrior goes quicker, thanks to the mine you built. He comes on turn 9 and on 10 a new citizen appears, which would throw an unguarded city on Deity into overpopulation disorder, and since your first warrior is out exploring, the second warrior should stay home to keep order.
After the mine is finished, the worker makes a road on the mined square, and then goes on to mine and road (in that order) a second shield-on-grass square.
This part might be controversial, but I think it's really paid off for me. After your two warriors, you build a granary. There is a counterintuitive part to this, though.
Just after you start your granary, your city will grow to population 2. At this point you will have one mine and a worker six turns away from finishing a second. During this time DON'T have your second citizen working a square that gives two foods. Have him work on a forest square. What's strange about this is that you're artificially trying to stagnate growth. You also finish the granary sooner, because a forest gives two shields per turn rather than the one you'd get from the unmined grass-with-shield.
The whole idea behind slowing your population growth is that you want your third citizen to come exactly one round after the granary is finished. I've calculated that you should keep a citizen working the forest spot for exactly six turns, and then put him back on the grass-with-shield, which should be one round away from having a finished mine. If the third citizen comes before the granary, or at the same time, it will take 10 rounds to make a fourth. However, if he comes in after the granary, it will only take five. This means that arresting development for a couple of turns actually makes your city grow faster.
After the granary is done you must make a settler. He is done exactly one round before your population would hit four, which would throw even a double-guarded city on Deity into disorder. After you shoot off your first settler, you will be very happy you built that granary, because your population will recover much more quickly, and you can fire off the settlers more frequently. They are by far the most important units to rush out in the early game. Sure, most of them are not protected from the barbarians, but one way to deal with them is to just always be broke. That way, they have nothing to steal from you. One way to get broke is to pay other civs for Wheel and Iron Working so you could make better decisions on where to settle.
Oh, and after the first settler, I usually build a temple, so that you can support more population. When I'm done the city is full and I do a second settler. Then barracks, then settler, and only after that I build proper combat units (interspersed with settlers and workers to relieve population density).
Anyway, everything after the first settler you can just make up, but up to that point, I'm convinced this is the optimal method.
This advice is most relevant to someone playing on Deity, though it will be useful for other contexts too.
I assume that there are at least three grass-with-shield slots inside your capital after the first border expansion, and at least one is available before.
First you set a citizen to work the grassland with shield while making a warrior. Then you take your first worker and assign him to dig a MINE on that spot. Meanwhile, the warrior pops out. He's not needed in the city yet, and has about 15 turns to explore the neighborhood before he needs to come back and prevent disorder at pop=3. The second warrior goes quicker, thanks to the mine you built. He comes on turn 9 and on 10 a new citizen appears, which would throw an unguarded city on Deity into overpopulation disorder, and since your first warrior is out exploring, the second warrior should stay home to keep order.
After the mine is finished, the worker makes a road on the mined square, and then goes on to mine and road (in that order) a second shield-on-grass square.
This part might be controversial, but I think it's really paid off for me. After your two warriors, you build a granary. There is a counterintuitive part to this, though.
Just after you start your granary, your city will grow to population 2. At this point you will have one mine and a worker six turns away from finishing a second. During this time DON'T have your second citizen working a square that gives two foods. Have him work on a forest square. What's strange about this is that you're artificially trying to stagnate growth. You also finish the granary sooner, because a forest gives two shields per turn rather than the one you'd get from the unmined grass-with-shield.
The whole idea behind slowing your population growth is that you want your third citizen to come exactly one round after the granary is finished. I've calculated that you should keep a citizen working the forest spot for exactly six turns, and then put him back on the grass-with-shield, which should be one round away from having a finished mine. If the third citizen comes before the granary, or at the same time, it will take 10 rounds to make a fourth. However, if he comes in after the granary, it will only take five. This means that arresting development for a couple of turns actually makes your city grow faster.
After the granary is done you must make a settler. He is done exactly one round before your population would hit four, which would throw even a double-guarded city on Deity into disorder. After you shoot off your first settler, you will be very happy you built that granary, because your population will recover much more quickly, and you can fire off the settlers more frequently. They are by far the most important units to rush out in the early game. Sure, most of them are not protected from the barbarians, but one way to deal with them is to just always be broke. That way, they have nothing to steal from you. One way to get broke is to pay other civs for Wheel and Iron Working so you could make better decisions on where to settle.
Oh, and after the first settler, I usually build a temple, so that you can support more population. When I'm done the city is full and I do a second settler. Then barracks, then settler, and only after that I build proper combat units (interspersed with settlers and workers to relieve population density).
Anyway, everything after the first settler you can just make up, but up to that point, I'm convinced this is the optimal method.