I settled my first city to the northwest (wheat) and built The Great Lighthouse soon after. That wonder is completely broken on Archipelago maps, and I used this to get lots of trade route bonuses from Gilgamesh, Mansa, Augustus, Elizabeth, and Catherine (Alex was Annoyed/Furious with me the whole game but was completely irrelevant.) I did neglect exploring with workboats so my trade route income was lower than it should have been. Nonetheless, I still won the circumnavigation bonus.
Regarding settling, I crammed in about 7 cities on the starting island, had a few more in other island locations, and even managed to get a city on Augustus/Mansa's landmass (but I didn't get the stone on the other island as Catherine got that). In general, I favored more cramped cities due to the Great Lighthouse.
I beelined Liberalism and Rifling. Fortunately, Mansa decided not to get Liberalism which meant I got Nationalism as the free tech (but didn't get the Taj, Elizabeth got that). I won the Music Great Artist race, though, and used two Golden Ages to help me get to Rifling. I also built the Globe Theatre in the southern city with two fishes and one whale resource (it has only one land tile, the city center, so I had to built it via whipping catapults and adding the overflow hammers.) Then I whipped/drafted and declared war on Augustus using a two-pronged attack. The first was land-based using the city I founded on his landmass to his south. The second was a naval attack to his north. My rifles/trebs had little problem wiping out Rome.
While this happened, Mansa vassalized Augustus, causing him to declare war on me. Mansa was technologically advanced, but I had more rifles and now cannons, and proceeded to take two cities on his peninsula (including his capital) and then I decided to call it a game.

It was fun. And I did not build a single cottage the entire game.
Sorry for the lack of screenshots -- I played this on a Mac computer and I couldn't figure out how to get screenshots.