Maybe the LJ brain-trust can provide some recommendations? Here are the titles I've particularly enjoyed:
ANIME: CardCaptor Sakura, Love Hina (the TV run, not the specials/second series), Cowboy Bebop (when it wasn't about Spike vs. Vicious), the first run of Comic Party, Ruin Explorers, eX-Driver, and of course the golden oldies from the dim-dark past such as Kimba and Speed Racer, although I'm not sure how I'd take to them if I was being introduced to them now
MANGA: Love Hina, Comic Party, DramaCon
What I tend to like are more comedies or light adventure pieces that delve occasionally into just enough drama to give them weight. I don't like things like Trigun that start out funny and then turn into a giant emo-fest halfway through. And I definitely don't like gore spewing all over the place, which can be a problem.
Whattya think, those who'd know?