Probably should have been:
Tommy Gambino because he was the Heir to the throne and married to Luchese.

Than Neil, because Tommy, was so weak Neil, would provide the muscle.

Paul #3 and in charge of the while collar rackets

Each provided a different purpose and should have not stepped in each other.

Meaning Neil, had no interest in running white collar rackets.

Paul had no interest in being the work horse crew that admin needs to keep everyone in check.