The Sicilian has cameos by Michael and Clemenza. In terms of order, I don't know if there is a definite order either. I've read The Godfather and The Last Don (which I thought was very good), and I'm in the middle of The Sicilian.

Just a note on The Last Don- even though I liked the movie, I liked the book more because the movie, in a sense, let the cat out of the bag in the beginning, so to speak.