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.

I actually watched Evangelion (+ EoE) first and while it did confuse me, its bizarreness got me interested in anime.

Had I watched one of those boring schoolkids comedy shows people here seem to be so obsessed with first, I'd never have given anime a second chance.