Depends on the situation actually...
If you have the room for expansion do so, but if you are going to end up having a bunch of underdefended cities the AI will (rightly) decide that you are ripe for the picking. Always send out a military unit with your settler to defend the city when it is first made.
Try diplomacy...I find that trading a single luxury good is enough to get on the AI's good side...heck if you cannot trade it give it to them. The best way to make sure that you don't get attacked by multiple AIs is to make friends with them...trading luxuries, right of passage, mutual protection, trades of a higher tech for a lesser one. Offer something to the AI to see what he is 'willing' to pay (though you can almost always adjust that amount upwards in your favor) then cut him a better deal...ally with an AI against the rival he is making war on (I'd always pick the weaker one in your shoes...) Diplomacy is much bigger in this game than in previous incarnations...
I even like to give gifts to the AI when they are fighting a war that I am not involved in...offer the Persians gunpowder when they are fighting the French or something, makes the Persians happy, helps take the French down a peg or two. Give the Zulus enough gold to enlist someone else's direct aid when they are fighting the English...stuff like that. Afterall, you are most likely going to end up in a war sometime, its best that you've got some friends to help you. I believe I read somewhere that Civs 'remember' things for 100 turns or so, depending on the action.
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Furthuremore, switch to Republic asap. Reduces corruption, increases production. At least, that is what I try to do.
I almost never switch to Republic until I've got a great infrastructure. If I am on good food producing areas I rush build like mad in Despotism until every city has a barracks, a temple, a granary, and preferrably a library and a marketplace. Then I go for the luxuries and switch to Republic (you need the luxuries because your military units won't keep the peace anymore and your people will be slightly annoyed with you for the rushbuilding (they stay annoyed for 20 turns/job I think). If I cannot get access to a couple of luxuries I switch to Monarchy instead so that I can keep the peace with soldiers and get the terrain benefits.
For me, switching government types too early actually puts you behind the tech race, especially if you aren't scientific (with the cheap to build libraries!) Its better to spend one population point out of a city of 6 than it is to lower your science rate so that you can afford to rush a library under a different government type. If your city isn't on a river it cannot grow past 6 anyway, might as well turn some people into an aquaduct so that it can continue growing rather than have to wait until you've got several hundred gold to buy one.
However if you have a really good starting location with lots of rivers/roads/luxuries and you are scientific switching to Republic is a good way to go...you can generate the cash you need by trading luxuries for gold/turn and sell off advancements to your 'friends' as you get them for max profit...I just generally am not that trusting and am involved in a war by this point
