I'd include, in order of preference:
--The Bocchicchios and how they helped Michael return from Sicily.
--Neri's story, and his rise in the family.
--The Don's war with Maranzano.
--The Don's move to Long Beach, including the "boiler inspectors" and Sonny's extension of "protection" to the community.
--Kay's departure to NH after the Great Massacre of 1955, and Hagen's visit to bring her back. This is very important because Hagen explains why Michael had to kill Carlo. If included in the films, it would have explained why he had Fredo killed, as well as all the others.
I could do without most of Johnny Fontaine, and all of Nino, as well as Jules and Lucy.