@sir_schwick: I don't think it's good to pop-rush any unit at this stage. Archers cost some shields, and if our pop is high, the city could built them quickly every time. We'd severe cripple our growth if we rush units, at the cost of citizens.
If we decide to go to war, we should focus on high shields, so we can produce archers faster, otherwise, if we rush units, we'd be at an even level with the AI who's trying to make settlers(loosing it's power from growth).
We could start building a settler later, when our capital has high pop, like 4-5 or more, if we can afford to raise the lux. By then, we should have taken the first Incan city.
What do you think of settling near the wheat at some point and build a granary?
I still don't understand the value of attacking with warriors. The AI would have spears, why should we attack with warriors? If you think, that we'd upgrade them later, i'd like to upgrade our warriors later too, but there wouldn't be any warrior left to be upgraded, if we go against spears.
Archers haven't good defence, but they have 2 offence, and they can "behave" like a catapult, if attacked. Better have our cities with high pop and shields and build them quickly and in sufficient numbers.
6-8 archers should be enough to take at least the Incan city close to us, move forward, while our cities keep sending reinforcements. Gather them together, and be outside their borders, when we'll declare, then enter inside and step on that hill.
btw: team-mates: nobody forces you to accept my plan, we could decide another approach to the game. I just made a judgement that we should go to war early, because we have crappy land for a settler factory(but with high shields for our current cities), AND(more important) we have an AI right next to our starting position.
I'm still not familiar with C3C and it's gambits, because I haven't played so many games in C3C. I've read about this "Republic gambit", where you get a free tech if you research CoL and Philosophy first, and then you get to choose a free tech. We should run the highest science we can afford every time, so we get that advantage?
Suggestions?
EDIT: The Incan UU is 1-1-2, which means, can kill and go away, or retreat if losing. At least, archers would "bomard" first.
Really, feel free to suggest another plan or approach to the game. I think, each of you has a plan in his mind. Just tell it. sir_schwick stated some thoughts, that's good. We have enough time to discuss.
Our UU is the NM, so we can't build spears(like Greece can only built hoplites). That's changing our plans. DON'T build them(not now, anyway: we want to avoid a despotic GA). We could go as soon as we have 6-8 archers, while our cities would constantly built units.
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Sometimes, the "little" Goebbels that's hiding inside me, takes control over things! 
