anime for the anime n00b?

Absolutely nothing to do for the next 3 weeks, so I've decided for the first time ever to delve into the world of anime.
What's really popular out there?
What are your favorites?
How would I go about watching these animes?
P.S. erotic content is fine (appreciated =D) but only as long as it doesnt take precedence over the plot, so dont give me hentai please.

>>41
Hellsing = Vampiric DRAMA and Elfen Lied is ACTION? Hellsing had many dramatic elements, but it was more action oriented and often those dramatic elements were used to enchange action. Elfen Lied on the otherhand is kind of like drama, harem and action(although not so much). I would describe bizarre mix as harem series for gore lovers and I liked it.