If you're a guy then definitely a shonen. I've watched anime sporadically on TV for years before I've gotten into them more seriously and all of anime that were showing were shonen, and for a good reason. Shonens are easily digestible, they're stories about struggle between good and evil typical for all of cultures.
Like in Daniel's case I too watched Naruto and since Jetix (good old Jetix.... :'() was rolling them out slowly I've wanted to watch them more regularly it prompted me to look for more episodes online. Now granted I've previously did the same with Dragon Ball Z but Naruto made me look for other anime.
My suggestion for a beginner's anime would also be Naruto, Bleach and/or Hunter x Hunter (probably my favorite shonen).
However, I'm not sure how girls approach anime... I've been wanting to get my GF to watch some with me but it's kinda hard to pick where to start... I'll definitely show her Clannad eventually since it's my favorite anime but I was thinking and right now I'd like to show her something else first so she'd have some basic knowledge or an idea what to expect. So for girls I'd suggest animes like Kokoro Connect, Myself;Yourself or SAO. But since I'm not expert with girls anime I'd like to get some girl's feedback as well, ladies??