If things had gone the way Vito Corleone wanted, the family would split under Tessio and Clemenza while the Corleones would keep their influence thru one of the three sons. His goal was for one them to be pulling the strings thru some other device other than corruption. He had hoped it would have been Michael that achieved this.

This infact did happen by the IIIrd film. Michael had relinquished all his illegal activities while still keeping a loose reign on the remains of the empire which had now been broken up into smaller pieces.

If Sonny and Fredo had lived -- I'm sure they would have used their GENCO experience [once it was completely phased out] in other enterprises to help the family.

As far as a successor, there would not had been a need for one, but, unfortunately, there was not enough time for the Don's plan to be completed.

"There just wasn't enough time."
"We'll get there Pop."