If you are looking for a classic comic to pick up I suggest Batman Year One published in 1987 by Frank Miller, art by David Mazzuccheili. This book tells the story of Bruce Wayne's first year back in Gotham after his training abroad and subsequently his first year as The Batman.
But it also tells of James Gordon's first year in Gotham. This book is an iconic telling of Batman's beginning and I very much enjoyed it. The real-time progression of the story is an interesting narrative device that really adds to the realism of the story. I also liked the establishment of Batman's relationship with James Gordon as well as the story also following Gordon's point of view throughout the year. All and all, an excellent book.
Now why I think a new comic book reader would like it is because this book really sets up Batman. It takes what fans know: his parents were murdered so he dedicated his life to learn how to best fight crime. And it gives the reader how Batman first used the skills he acquired and how he became a potent force in Gotham.
If you do end up reading this book and are craving more I first of all suggest watching the 2011 animated movie Batman Year One, the movie stays true to the book and I think it is a great adaptation of the story. I also suggest other works by Frank Miller, he was an iconic force in the 80's as he also wrote the wildly popular 1986 stand alone story The Dark Knight Returns.
I'd give this book a Must Read rating.
Thanks for taking the time to consider my thoughts-
Grant Crawford