It's no mistake that an alphabet of letters is called a typeface. Like the human face, subtle differences in the cut of a type family creates different moods and personalities.
The mood or personality of typeface can be an important part of storytelling. For instance, the association of the number 11 with the World Trade Center buildings. The choice of a serif typeface would not have been an ideal type choice. Using a sans serif uppercase letter 'I' in place of the numeral was an obvious choice.
Typography also can be associated with time periods, such as the funky bubble type seen in1960s advertising, and the almost unreadable type that appeared in Ray Gun magazine during the early '90s. Use these only when the story calls for it.
Just as an exercise, take any word and change the typeface to several different styles and see how the mood changes. Generally, serif typefaces look more formal and elegant, while sans serif is more modern and youthful. Display faces have multiple personalities, and are usually used in larger sizes because they aren't as legible when used for text.
The most important part of using type is making sure that it is a reflection of, and enhances, the story. I wouldn't recommend that you spend your time scrolling through your type library looking for the perfect style. But, exercises like this will help improve your recognition of the big and small differences that give typography personality.
Great piece on the importance of well-chosen typography. I think...