three types of persons, entities, or professions traditionally

I think you can look at the characters in The Great Gatsby in terms of class. The three different "types" we see in the novel are pretty apparent from the get go. First, you have the East Eggers; they're wealthy (old money). Then you have the West Eggers (new money, not considered appropriate for old monied people to befriend). Thirdly, we have the people living in the Valley of Ashes (poor, working class), and finally, the hangers on (people like Jordan, Owl Eyes, the piano player, and the other party goers). These were the characters who just kind of went along for a ride on the money train.