I think Portugal might actually be my favorite BNW civ. Naus are very cheap to produce, and with a solid amount of hammers in say, 3-4 cities, you can churn them out every couple of turns and send them straight to the other side of the world to sell their goods, before exploring the map. You'll be likely to found the World Congress, and come the Industrial Era, you're going to be able to buy yourself a nice city state with Coal and get first Ideology too. Personally, I'd recommend going Freedom, for Arsenal of Democracy, and just keep crapping out Naus, selling their goods, then gifting them to city states for the influence. You can maintain control of every city state with absolute ease and just, run away. Last game I played, I went for the Diplo victory because uh, why the hell not, but I could've quite easily turned that advantage into a Science Victory or a Domination Victory with all the extra beakers I was getting from my allies, and the absolutely insane size my capital got to with all the Maritime city states and the internal trade routes I was directing to it (50+!). Hell, my culture wasn't doing too bad either, by the time I was waiting for the timer to run out on the World Leader vote, I had a bunch of the dirty communist cities of Germany and America flip to me.
So yeah, summed up: I love Portugal and you should too.