Personally, I am a huge fan of Fables. It's not a superhero comic book, it's about fantasy characters such as Snow White and the Big Bad Wolf who all live together in a compound in NYC. It's funny and smart and generally really cool.
I love the classics as far as comic books go. I would either start with Batman or with X-Men. In both of these situations you will have excellent storylines and will have a hard time running out of reading material
The Watchmen is a classic comic book series that is almost universally beloved. If you go to Barnes and Noble you can buy a book which includes the entire series. This is my recommendation for a good comic book to read if you are new to comics.