Re-reading the opening page of the story I'm working on, I realized that although I have a paragraph in there introducing the character that you play, the information that you learn has almost no impact on the rest of the story whatsoever.
In general, do you think that it is better to: a) give the player a particular character to play; b) give the player an anonymous character to play, allowing them to be "themself"?
If a), how important is it to make sure that the particular characteristics of that person are relevant to the story?