Hmmmm,I like the idea of brainiac being created from the crystals kitty threw out..he absorbs the knowledge of the crystals,learns of earth and Kal-el from them..he studies earth, learns of lex,and seeks him out.he makes N.K. his ship,and transforms it to suit his needs.he is also just as strong,if not stronger than superman.
When Lex and brainiac first meet,Lex could/would name him.Brainiac wants to make earth a place for machines,with no room for humans.He tricks lex into helping him,by making him think he wants only to overthrow the humans,and rule them with lex, not destroy them.
Brainiac learns of jason from lex,and kidnapps him.he wants to study the half human/kryptonarian,and experiment on him.
first encounter between supes and brainiac involves a huge city,and state wide fight,with supes losing,and nearly killed.metropolis is in ruins.fires,smoke,and demolished buildings are everywhere.
you could have an apperance by a powerless Zod in prison.Since he knows the technology of krypton,supes goes to visit him after he recovers,and in exchange for his help in telling him about the AI,superman offers Zod freedom.
Later brainiac finds out,and kills a powerless zod.Lex would discover brainiac's true intent,and would help superman defeat brainiac,but only to save himself.
After a second huge fight brainiac is defeated,using the knowledge zod gave superman. Then Supes searches for jason and finds him in brainiac's Lab in a coma,mutated,and nearly grown.Supes blames himself for not saving his son first,instead of metropolis.
(jason could be who ever the reader wishes,since several like different villians)