This is how I saw Zod's character develop
- Upset with the council's direction that has led to the coming destruction of Krypton, Zod attempts a coup to overthrow the Kryptonian council, put himself in charge, and select specific bloodlines to rebuild and continue Kryptonian society.
- After being released from the phantom zone, Zod goes to various Kryptonian settlements to look for survivors/signs of life, perhaps a suitable living environment.
- After Kal-El accidentally sends a signal to Zod's ship, Zod travels to Earth, confronts Kal, explains to him his intention to remake Earth into a new Krypton, while exterminating the lesser species on the planet, the humans.
-After world builder, the Kryptonian ship, and the rest of the Kryptonians are killed/destroyed/moved to the phantom zone, Zod, losing his sense of purpose, goes insane and decides his one goal in life is to kill the human race because of his hatred for Kal-El for essentially ending the Kryptonian bloodline. This is really the only time his motives turn to revenge.
I mean, I think at the very least that's very serviceable and a lot better than the majority of villains in comic book movies.