According to the creator of the neighborhood, Reckless Jerry on Mod The Sims, there is no play order for any of the families in Disarray Harbor.
That being said, after playing the neighborhood myself, here are my suggestions and why. You’ll also learn about all the family dynamic’s, relations and drama. You don’t have to start with any family in particular with each dynamic below
The Markovich’s, The Masons, and The Black Families
Family Drama #2
The Banners, McMillian’s and The Whites Part Two
Family Drama #3
The Chesterfield’s Part One & The Chesterfield’s Part Two
Family Drama #4
Family Drama #5
Family Drama #6