My typical style is to build as many cities as I can sustain as quickly as possible and equip them with archers for defense, as mentioned before, because I know any neighbors I have will be gunning for the land/resources I am aquiring.
Once I have a large empire of land & resources which is defended by archers (or the equivalent for my tech level) I'll make sure to turn on the charm and build everything I can with happiness and gold in mind. If I notice a neighbor getting itself equipped with a large military, I'll build more defensive units as well. During this period I will be firendly, peaceful and trade freely with those who are willing to pay or make good bargains but I always refuse demands or unfair trade deals. This lets me eek out an inkling of what AIs are doing in their own empires, either languishing, thriving or making war preparations and being aggressive. I'll remember those impressions for later in the game.
If I get the technology edge, my people are happy & no neighbors threaten immediately I will turtle up and go for a science or cultural win. If however I can see a fight is inevitable I will build up a powerful military & wait for the DoW. I like to puppet cities and pick off attacking enemy units to the point where my foe is offering me the moon for peace, where I'll turn their attitude around and make them friends and trading partners for the remainder of the game.
I have never really gotten the hang of being a warmonger on my own but when given the chance to build up a strong, economically potent empire I can turn the tide and roll out with a big military as needed. I kind of think of my style as being like that of the United States in the first half of the 20th century... Strong enough to survive and adaptable enough to overcome.