I guess I first got into manga when I was in Japan back in 2000. I was browsing a shelf mindlessly, and one series happened to have very striking art, so I bought a few, although I was pretty embarrassed to bring some books to the counter with a name like "Love Hina". Imagine my surprise to see that Ken Akamatsu's stuff became popular overseas a few years later.
I usually gravitate towards series that have very clean, nice art styles. Even if they have great stories, I can't take stuff that have really sketchy, crude looks.
Battle Royale is probably the best overall series I've read. Each time a new volume would come out, I couldn't put it down all the way to the end. Although it is a little silly to think that these are supposed to be 9th graders doing these things...
Gunsmith Cats is good too.