ZOMBIES 
Do you dig zombies? Have you ever wished that
George Romero's films kept their edge, but had better character development? If so, you’ll want to check out
The Walking Dead. It’s a “post-zombie” story, so it is more concerned with the survivors of a zombie apocalypse trying to go on with their lives after society has collapsed. It’s extremely character-focused and incredibly well-written, making it all the more shocking when you realize that absolutely no one in the series is safe from being killed. The realistic art pulls no punches, though, so if you can’t handle much gore, you might want to look for something a bit lighter.
Thankfully, I’ve got just the right thing for your softer side.
CUTE ANIMAL STORIES
There is nothing cuter than
Owly, which is one of my wife’s favorite book series. It follows the world’s cutest owl (Owly) and his unlikely best friend (Wormy) through a series of gore-free adventures. It is so adorable that you may want to throw up from overexposure to cuteness. The best part is that the stories lack text dialogue, making them a great introduction for early readers to the joys of sequential storytelling.
Plus, the creator,
Andy Runton, has lesson-plans available so that you can even us Owly in the classroom. Now, if that is a bit to saccharine for you, we can swing to the exact opposite end of the spectrum with one of the most influential and disturbing comics of all time.
FANTASY/HORROR
Neil Gaiman has developed a very loyal fan base outside of comics with his films and novels, though his
Sandman series is one of his most endearing and influential works. It is one of the original titles for DC’s Vertigo imprint, which prints
Y: The Last Man and
Fables.
This high-fantasy series follows
Dream (the mythical Sandman) and his family of equally as ethereal beings (including his sister
Death, who eventually became one of the most popular characters and spawned her own series of books). The art and style is a bit dated if you are used to more contemporary work.
The early volumes are all extremely dark and horror-based, but as the series progresses and it becomes focused on Sandman’s growth as a character, it delves more into mythological exploration than sheer shock value.
AUTOBIOGRAPHY/ANTI-ROMANCE
My wife’s absolute favorite graphic novels are all by
Jeffery Brown, who writes a series of autobiographical graphic novels about failed relationships and general heartache. His style is really simple, but intensely relatable.
Brown’s work is almost all printed by Top Shelf, whose off-beat, “real world” comics are amongst the most creative and innovative books on the market. Brown’s work has a tendency to be melodramatic, but his open and honest approach is refreshing and emotionally resonant.
The best place to start would be with
Clumsy, which tells of the rise and fall of a burgeoning relationship with all of the warm-fuzzies and cruel brutality you’d expect from the reality of a real romance.
MODERN SUPERHEROES
It’s hard to recommend any superhero books to new readers (especially women) because they are so interconnected and rely too much on stories from the past. Still, superhero comics are the cornerstone of the comic book industry and so I am often asked where the best place to start for new readers is. I always fall back on
Batman: The Long Halloween and
Batman: The Killing Joke.
Long Halloween takes place during Batman’s early years so it doesn’t require previous knowledge and reads more like a good mystery book than a superhero comic, despite being filled to the brim with some of Batman’s most famous villains.
The Killing Joke is my all-time favorite superhero book and is clearly one of the key inspirations behind
Heath Ledger’s Joker in
The Dark Knight. In the story, the Joker tries to push Comissioner Gordon as far as he can to prove that any sane man can snap just like he has, but in the end only Batman can truly be as crazy as the Joker. It’s pretty shocking, but incredibly captivating.
Of course, you can also always try
Watchmen. I don’t recommend this right away because it is extremely dense and most of its effectiveness comes from its deconstruction of the superhero genre. However, there is a reason why it is considered the “Holy Grail” of comics and is arguably the best superhero story ever told. You’ve got some of the most engaging characters in the history of the medium being written by its all time greatest writer (Alan Moore) and being drawn by one of its most competent artists. It is required reading for all superhero readers, but isn’t something I’d recommend jumping into right away.
CRIME 
Crime comics are getting to be a pretty big genre these days and a lot of the books that are popping up are really good. My absolute favorite of these is
Criminal, which is put out by Marvel’s Icon imprint (which is like DC’s Vertigo in a lot of ways). Each volume of Criminal is a stand-alone story, though they all take place in the same “universe” and feature a few cross over characters. Unlike most crime stories, this series follows the criminals rather than the folks trying to catch them. The lush, grizzled artwork by
Sean Phillips is the perfect compliment to
Ed Brubaker’s atmospheric writing, with the brilliant colors by Val Staples being the icing on the cake of creative awesomeness. Reading it feels a lot like watching an extremely good movie. There are four or five trades out now and all of them are simply fantastic.
I’d also recommend
100 Bullets, which is much longer series (13 volumes covering 100 issues). It combines the pulpy crime elements of something like Criminal with a massive conspiracy theory laden story. It has a huge cast that is all interconnected, so if you take breaks between reading volumes, it can be pretty easy to get lost. However, I think a lot of libraries actually stock the full set, so it might be pretty easy for you to snag them in succession with few delays.
REVISIONIST LITERATURE/HISTORY
Since we are working under the assumption that our new reader has read
Fables, they will already have a handle on this concept already. Since they probably liked Fables, they should also love
League of Extraordinary Gentlemen (don’t worry, even though the movie was horrible, the comic is amazing).
Instead of fairy tale characters, this is about the best literary characters from the 19th century including Mina Harker from Dracula, Allan Quartermain, Captain Nemo, Dr. Jekyll, and the Invisible Man joining forces to save Britain from the likes of Fu Manchu and Doctor Moriarty (the nemesis of Sherlock Holmes).
Plus, it is written by
Alan Moore (who I referred to earlier as the single greatest writer in the history of comics), so you know that it is amazing. As with all of Moore’s work, this does not pull any punches, though, so don’t expect it to have the same fairly tame appeal of the stories the characters are pulled from—especially in the second volume.
PURE AWESOMENESS 
One of my absolute favorite graphic novel series is Bryan Lee O'Malley's
Scott Pilgrim series, which is a manga-inspired tale of a Canadian slacker musician who falls for an enigmatic American delivery girl and must fight her 7 evil exes before he can officially be her boyfriend.
The books cover a number of genres, including action, comedy, and romance, with a number of twists on each. There is a movie coming out next year starring
Michael Cera and directed by Edgar “I directed
Shaun of the Dead and
Hot Fuzz, so I’m clearly awesome” Wright, so the volumes are showing up in big chain stores now.
The books are quirky, energetic, and feature some of the most memorable characters I’ve ever read. I get giddy just thinking about how awesome these books are and love them so much that I actually named my hamster after the lead character.
MY ABSOLUTE FAVORITESo, you've decided that your only goal is to make me ridiciulously happy with your next read? Well the best way to do that is to read and love
Preacher. It’s amongst the single most controversial, offensive, and thought provoking comics that Vertigo ever published and they are pretty known for controversial, offensive, and thought provoking comics.
The story follows
Jesse Custer, a preacher, who is granted incredible powers after a demon and an angel have sex and create an entirely unholy. Not crazy enough for you? Well, then you’ll be glad to know that he decides to use his powers to wage war on God after he realizes that the Almighty has abandoned us.
Still not crazy enough? Did I mention that he is joined by his alcoholic Irish vampire best friend and former assassin girlfriend, and that they are being pursued by a secret Christian military and the “Saint of Killers” (God’s personal hitman)? It’s a modern Western and simply amazing. I know it sounds crazy, but I can’t recommend it enough. If I was trapped on an island and could only take one complete comic book series, it would be Preacher.