Most of us have an intuitive understanding of the history genre. It serves in a way to take us back in time so that we can observe what happened at a particular time and place. In the Old Testament the books of Samuel, Kings and Chronicles serve as clear examples of the history genre. In those cases the history spanned several generations and covered the kingdoms of Israel and Judah, not a portion of a single man's life as in Jonah. Unlike those texts, there is no evidence that Jonah's author relied on archives or other written sources, but either had access to a witness of these events or some oral tradition.
Perhaps a more likely candidate for a story of one man would be biography. Modern biographies aren't all that different from history or journalism in that they focus on accurate and complete details. Ancient biographies were less concerned about strict accuracy—often they included clearly apocryphal stories that illustrated some personal characteristic of the subject. For instance, one of our prime sources for early Roman emperors, Suetonius's On the Life of the Caesars, includes a number of omens and dreams that seem fairly unlikely. But in either era, biographies attempt to draw out the meaning of their subject's lives and selects details that illustrate that meaning. Ruth, Esther, and sections of other books such as the lives of David, Joshua, Daniel, and Joseph are Biblical examples of biography.
Perhaps a more controversial theory is that Jonah is a parable, or at least is told in the form of an extended parable. Although characters in parables are usually unnamed, Jesus christens one of his protagonists "Lazarus". The introduction and conclusion of Job may be regarded as two halves of a parable as well. The key to identifying the genre is to recognize lesson or point of the story and notice that all details emphasize that point. The other genres tend to include details that would seem extraneous to reason for telling the story. Jonah is notably light on extra detail.
Selecting the parable genre does not mean finding Jonah to be fiction, but it does indicate whether historical accuracy was held sacred by the author. Though we aren't used to this way of thinking, miracles such as living in a whale for three days, increase the odds that a parable is based on reality. The reason is that parables were constructed as simple, everyday stories that an audience could easily grasp so that the hidden, more complex meaning would be more clear. In Jonah, the story of the whale adds little to the deeper meaning and would not have been familiar to intended audience. Even today, we see that the "fish story" element tends to swamp the ultimate meaning in the text. An author starting the story from scratch would probably found some other way to turn Jonah back to Nineveh. A simple solution would be for the sea to become calm as soon as the sailors began to return to shore.
Of course God did not do things that way because the story of the whale becomes the "Sign of Jonah" for Jesus many years later.