Zombie game is too broad of a subject, it’s the same as saying “What should a ponies game have?” but in the end…
Will it be a 2D or 3D game?
Do you have a genre in mind?
I advice checking for commonly used genres, survival is becoming extremely popular with the DayZ
Do you intend to have Zombie killing or simply “run away”?
Do you intend to have mutated zombies?