Which do I read first

Did the eternal storyline happen before the main new 52 batman

No, it’s after Court of Owls/City of Owls. I think it’s after Death of the Family too.

Batman #36 starts a story that follows the events of Batman Eternal. When it originally came out I stopped at #36, read Eternal, and then finished the last 14 issues. But its still a good read whichever way you choose to read it.