It is very important to play first. Is there randomness? yes, it is there to every player. Everybody gets the same dice and the same cards to choose from. If you play first, you choose the cards first, you get to move your ship first, and to buy a quarter first. Then, there is a great chance you'll win the game.
There is also one more thing as much important as to play first. Making good plan when choosing the right dice, specially in the first rounds. If you manage to choose well your dice, but not playing first, you still have good chance to win, since there is a lot going on at the sea and at the city to compensate that.