@Matthias: Overall some good advice, except for one significant bit: The starting build should NOT go warrior->warrior->settler. The only time you want to start out with a build like that would be if your capital was low on food but very close to a location with high food. Since Babylon has bonus grasslands and a grassland cow, building a granary before the first settler will generally lead to a better growth curve. So instead of warrior, warrior, settler, try warrior, warrior, granary, settler, and then either follow directly with another settler, or go with another military unit and then another settler. It delays your second city, but greatly speeds up founding every other city past that since you aren't waiting on population growth nearly as long.
@Shillen...Some rebuttal is in order. I'd disagree with a rush to the Great Lighthouse for this sort of map. With the 40% land archipelagos, you're about as likely to create some sort of twisted pangea or continents map as you are a string of islands, and in either case you probably don't even need Astronomy to make contact with other landmasses. This one in particular looks like it's at least a continent-sized starting landmass and it has at least three civs on it (Zulus, Babs, Iros), and probably room for more, since the Zulus hardly moved an inch towards Babylon in the 2000 years after founding Ululundi and AEnigma hasn't really yet hit the boundaries of this landmass with his scouts except for the northern shore. The fact that the Zulus founded exactly one city closer to Babylon than Ululundi also invalidated some of my reasons for choosing my red dot first, that being to help shut off the rest of the continent and establish a more favorable border against Zulu expansion. In that case I'd probably lead off with the gray dot, then the blue and yellow dots, before picking up the red dot and finishing out my list.
Is this a large map or a standard one? I can't really tell from the minimap. If it's a standard map, then my green dot or maybe one city's length further out into the fog is about as good as you can get to build it by hand, but you can probably go out a little further on a large one.