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My favorite stragity is to take the caribian islands (and killing all the indains on the islands). Once you clear the islands, you are safe from indain attacks (they always get ticked off and attack me anyways). Movement is faster over the sea and the alantic is right there for shipping back to europe. Then you can fish all you want and they cannot fortify next to your cities to block your fishing due to fort/fortress attacks. There is also only one or two squares that they can land on and you can attack at your own pace. Any cross town shipping (or reinforcements) can be done by leaping from port to port so your merchants are always safe. Also, I always have a massive fleet alowing me to sink their boats and trap half their army back in europe!
The downside is once they invade, you lose your wood source and only get 3 moutains or hills to work with.
Lastly, don't try to fill all the squares on the islands as the attack forces will just ignore whatever you have there and land anywhere. It will work against the other three powers though.

I also recomend keeping large merchant ships fully loaded with horses so you cannot run out.