It's really that easy: Viz Media has a great digital deal going on until November 20 for first-time customers: If you download their app (for iOS or Android), they will give you volume 1 of the series of your choice for free. Digitally, of course.
Naturally, I don't qualify for this, because I have had the Viz app since the day it came out, but if you're interested in that free volume, I have some suggestions.
If you're new to manga, and you like stories with lots of action, check out some of the Shonen Jump titles, which are among Viz's best sellers: "Naruto," "Bleach," "One Piece." But if you want some shonen action that's a little bit different, I recommend "Blue Exorcist." It's about a teenage boy who is studying to be an exorcist, but the twist is that he is, literally, the son of Satan. That obviously provides lots of conflict, and manga-ka Kazue Kato mixes in a bit of humor as well. He has a kind of crinkly, dynamic style that is surprisingly easy to follow as well.
Another shonen manga worth a try is "Toriko," the story of a Gourmet Hunter who travels to exotic places to find the rarest, best tasting delicacies. What makes this manga so fun is the amount of imagination creator Mitsutoshi Shimabukuro pours into coming up with exotic animals and plants for Toriko to eat.
"Hikaru no Go" is a longtime fan favorite, and for good reason. If you want to see manga genius in action, watch Yumi Hotta and Takeshi Obata make a story about a board game exciting. This manga is about a slackerish kid who gets the ghost of an ancient Go master stuck inside his head and slowly develops his Go skills, testing his abilities through a series of games and tournaments. Of course there's the alpha Go player that he has to beat, and lessons to be learned. Obata's art is clean-lined and easy to read, making this a good choice for readers who are just getting into manga.
Speaking of Obata, there are two series by him and Tsugumi Ohba that are both well worth a look. "Bakuman" is a manga-about-manga, specifically about two young men trying to make it in the manga biz. "Death Note" has a really clever premise: A bored shinigami (death god) drops a notebook for a mortal to find, and high-school student Light Yagami picks it up. The notebook gives him the power to kill people long distance, under a certain set of conditions, and he sets out to rid the world of criminals. The police quickly figure out that something is up and bring in the mysterious detective L to solve the mystery, and the manga turns into a clever cat-and-mouse game from there.
If shoujo is your thing, Viz has plenty to offer there as well. If feisty heroines are your thing, check out "Oresama Teacher," about a fight-prone girl who is sent off to boarding school for one last chance to redeem herself but can't help getting in trouble—always for the right reasons, of course. "A Devil and Her Love Song" breaks out of the usual shoujo tropes and gives us a smart, sharp-tongued heroine who speaks her mind and refuses to be bullied. If you want something closer to the traditional shoujo story, try "Dengeki Daisy," about a girl who is mourning the death of her older brother and is comforted by cell phone messages from a mysterious entity called DAISY. And if you want some serious vampire romance melodrama, you can't beat "Vampire Knight," an angsty tale of vampire guys and a human girl in a school that has classes for humans during the day and vampires at night.
Of all the shoujo bunch, though, "Jiu Jiu" is probably the best for a free trial, because it's a gamble: I loved it, but some other people hated it. It's the story of a demon hunter who feels all alone in the world after her brother dies, so her father gives her two wolves as companions. The wolves can transform into human boys, but they never really lose their canine qualities, which makes for some interesting drama as well as comedy when they follow her to school.
Finally, I have to say a good word for Natsume Ono's "Ristorante Paradiso" and the sequel, "Gente." They aren't Ono's strongest works, but if you're looking for something a bit quieter and more literary, some manga for adults, either of these is a good choice. Complete in one volume, "Ristorante Paradiso" is a soap opera set in a restaurant in Italy, where all the waiters are attractive older men who wear glasses; the main character is a 21-year-old woman who comes to confront her mother, the owner of the restaurant, who abandoned her as a child. Despite the explosive premise, the story is a bit weak, but Ono's elegant art makes this a manga worth reading anyway. "Gente" is a three-volume series set in the same world.
If you have a device to download the app to, now is the time to do it. I find the Viz app to be one of the best functioning comics apps; it's smooth and easy to use, and the manga look really good (especially if you are reading on an iPad, which is bigger than your standard manga page). The free volume 1 just sweetens the deal.