I just finished my first proper game, large, as a warlord, playing as Russia. First I had a rather small army, minding my own business, until the very large and powerful japan decided to declare war on me. Fortunately, the way to my civilization was through a mountain bottleneck, and I managed to plug that hole, and kill a lot of his attacking units. When he was weakened, I counterattacked, and suddenly he wanted peace. He wanted it so badly, he traded me all his cities except his capital. Got a bunch of puppet cities, annexed some, had to build a shitload of circuses to get everybody happy again, but then I had a huge empire, and researched a lot faster than the rest, too. And had a lot of money. So after that it was pretty simple to beat the rest.

City states are especially awesome if they were conquered by someone else, and you liberate them. If you are very large, you don't really need the extra city anyway, so if you liberate them you get all the bonuses for a long time. And i read in the civipedia that if the UN is built, all liberated city states automatically vote for you.