^ Civil War takes place about a third of the way through his tenure to date.
I'd recommend X-23: Innocence Lost
and (especially) X-23: Target X
The series are much better than the concept suggests. X-23 is a female near-clone of Wolverine (technically, she's his sister, though all of her DNA is his) created by a program trying to replicate the original Weapon X experiment. It's a much less niche story than it sounds. Her personal struggles - very different from Wolverine's are the heart of the story; hers is the story of a damaged child, not someone resisting a feral nature.