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.

Hmmm, hard to give you something you like without any idea as to your preferences. the titles I'll name will all be significantly different from one another in style

Series:
Great Teacher Onizuka
Samurai Champloo
Cowboy bebop(same director as SC, but episodic)
Rurouni Kenshin
Card Captor Sakura
Fate/Stay night
Serial Experiment Lain
Ranma 1/2
Fruits Basket

Movies:
ghibli shtuff (Princess mononoke(spelling?), spirited away, etc)
Akira(classic, obviously)
Ghost in the shell (1 and 2)

As for picking one you like, search for plot summaries to tell the general genre, but I we can probably steer you better if you'll tell us what you're looking for, for example answer questions like these:

Episodic/epic?

Period? (past/present/future)

Target audience? (G, PG, R)

Humor (serious(completely), intermittant/mild, slapstick)

Action/drama/romance?(all shows have drama I spose, but some have no 'fighting' so to speak).

I dunno, there are probably better metrics for classifying preference, that's just a few off the top of my head. My point with that is that there's a whole lot of popular anime, and if you narrow your aims you might get better results.

Lastly, how to go about watching them... Do you mean how to get them? Well, since the 'popular' anime generally is all lisenced in the US, downloading them is possible, but not legal. Rent/buy/borrow? The movies and fruits basket you can watch with the english sound(dubbed). In general though, if you have an option, subbed is generally considered to be better(because the dubs are generally really terrible voice acting).

As for erotic content with plot, if you mean fan service (randomly seeing characters naked) that happens often enough, if you mean a full on hentai scene worked into an otherwise 'normal' plotline, nothing comes to mind (though I'm not the otaku that some are).