I've been reading manga since elementary, so it's hard for me to come up with introductory works. On the other hand, I know a number of people who are interested in manga but intimidated by the large number of titles as well as the different format.
On the whole, I am going to suggest right-to-left titles. It may seem easier to start with a flipped work, but it's about the same learning curve. Manga, especially shojo manga, uses 'indefinite' panels rather than the strict rectangles of western graphic novels.
For those confused by 'indefinite' panels, see the above page from Aishiteruze Baby** (Yoko Maki). It might be a hard page to start with because there are a number of people speaking in the background in addition to the main action. You can still follow the flow of the art. The top right corner ends the previous scene, then the large art beneath it begins the new one. The next panel is the top left corner, followed by the bottom right, and ending with the bottom left. Though it's right-to-left instead of left-to-right, the panels and bubbles are still oriented top-to-bottom.
For those confused by the term 'shojo manga,' it simply refers to girls' comics. The other common division used in the US is 'shonen,' or boys' comics. There are other genres, but many of them blend into each other. The final determination is the genre of the magazine it was originally published in.
The other restriction I put on my selections is I limited myself to mostly happy titles. Saikano (Shin Takahashi) is a beautiful work, with spare art that seems to minimal at first, until you realize how well it fits the story. Of course, if you don't cry about once per volume of Saikano you have no heart. It's a bit to deep for a starting point.
Instead, I'm going to open my primer with a comedy: Haunted House by Mitsukazu Mihara.
Sabato Obiga just once a girlfriend, but every time he brings one home his family manages to scare her off. Both the humor and the moral translate well. Sometimes research into Japanese culture is needed to properly appreciate a tale, but no one could argue with the family's motivation. Mitsukazu Mihara has beautiful, stylized art well-showcased in a variety of series and one-shot volumes. I chose one of her one-shots because it allows for a lack of monetary committment. Her other volumes are more heavily influenced by Gothic Lolita fashion and sensibility and might be less immediately accessible.
My second recommendation is the bildungsroman (of a sort) Paradise Kiss by Ai Yazawa.
This series is contained within a mere five volumes, much shorter than Ai Yazawa's more popular NANA. Personally, I prefer it to that work. On the art side, Yazawa is top notch. Detailed, distinctive, and clear. She's also fabulous at characterization, need in this tale of first love and growing independence. Yukari just wanted to do what her parents wanted her to do, until she met a group of art students helmed by the charismatic and attractive George. She agrees to become the model for their "Paradise Kiss" label and soon begins to learn what she really wants from her life. I have yet to see the anime adaptation, but it's been reviewed favorably.
Next, I'm going to change gears with the much darker Death Note by Tsugumi Ohba and illustrated by Takeshi Obata.
Genius teenager Light finds the Death Note and decides to use it to create a utopia by killing criminals. Soon he's playing a game of cat-and-mouse with the world's best detective, known only as 'L.' This one is a bit more of a committment - twelve volumes total. The story is compelling psycologically and Obata's artwork is as beautiful as always. I used this one to start my dad on manga. Once you've finished the manga, there's an excellent anime adaptation, live action movies, and a light novel.
(Yes, that is from the anime - the dubbed anime - while this is about manga. However, it is just that epic.)
My next choice is again a longer series, but one worth the investment. Of course, I also encourage investment in the anime which goes in a much different direction. (Even as good as the anime is, the manga is better.) Primer choice #4 is Fullmetal Alchemist by Hiromu Arakawa.
Two brothers try to resurrect their mother using alchemy, but it goes awry. They want to restore their bodies using the Philosopher's Stone. The elder, Edward, joins the military to fund their quest. Unfortunately, things aren't very straightforward. This series will appeal to fans of science fiction and fantasy. Arakawa is an excellent storyteller and his art is a bit rough but flows nicely and is well-suited to the story. This one and Death Note are popular for a reason.
I think four is a good number, but I'll offer a few more suggestions:
Trigun by Yasuhiro Nightow: Great art, great story, western, sci-fi, and awesome. (Anime availabe and worth watching.)
Excel Saga by Rikdo Koshi: Possibly the wordiest manga ever. Utterly insane and requiring some knowledge of Japanese culture, but there's a handy glossary in the back. Once you're familiar with anime, manga, and have done some cultural research, watch the anime adaptation. It's absolutely hilarious, but the more you know the more jokes you'll get.
Nausicaa of the Valley of the Wind by Hayao Miyazaki: Beautiful, detailed art and a complicated by wonderful story about environmental protection in a post-apocolyptic world. The anime movie is one of my favorites, but it's compressing quite a bit into two hours.
Mushishi by Yuki Urushibara: Not sure how to describe this, except there's a reason it's won several awards. There's no overarching plotline, just a series of episodes, but they capture human emotion beautifully. There's also an anime and live action movie.
Okay, so Excel Saga might not be the best for beginners, but I had to pimp it. Feel free to disagree with my selections, suggest your own, or ask me for more!