You should definitely take a look at PR's entry on the 'Geek.
Puerto Rico is my wife's favorite game (out of about 100 that we have), probably because the competition is very indirect while still providing for some interaction. There is a lot more going on in PR than in Catan or Carc, in terms of available options at any given moment, but you'll find that there are optimal moves to be made in a lot of situations.
PR's popularity and high ranking on the geek are the subject of a lot of controversy, and there are plenty of articles to read on that. Most of the arguments center around those who think that the game has big problems because the person who sits to the left of the new player invariable wins (due to the new player not understanding that you don't do what's best for you on your turn, you do what's RELATIVELY best for you, given what you expect the remaining players in the turn to do).
Still, it is an excellent game, and I never turn down a chance to play (even though there are a lot of games that I would prefer). Do make sure you always play with at least three, however, as none of the two player varients really works well.
Take care to read the rules a few times before you play, though even then you should expect to get a few things wrong that you start to correct with subsequent plays.