Rivals For Catan – How do you draw a card when playing the Library
I would say that "choose a card" indicates you may look through a stack; otherwise, they would have been more specific and said to take a card from the top, or take a card at random, or something like that.  Admittedly, they could have been a little clearer.

According to this BoardGameGeek link, Professor Easy's Interactive Online Tutorial has an example where one of the players is shown using the library to look through a stack.  I must have clicked 100 "Next" links and didn't see that, but I spaced out near the end.