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.

Commercially wise
Trigun
Kenshin
Cowboy bebop
Full Metal Alchemist
Anything made by Miyazaki
Ah my goddess
Fushigi Yuugi
Fruit Basket
Evangelion
Slayers (all of it)
Hellsing (was ok)
Escaflowne
Gunsmith Cats
You're Under arrest
Full Metal Panic
Bubble gum Crisis
Vampire Princess Miyu (Do not watch the tv series)
Akira (yes good and bad)
so many to list.. ^^;

Fansub wise.. You can download via bittorrent
Ah my goddess season 2 tv
Ergo Proxy
Fate Stay Night (though it got licensed)
Blood +
Eureka Seven (got licensed)
Bleach (can miss gap fillers here and there)
Naruto (gap fillers must DIE!)
The Third
Le Chevalier D`Eon {looks very good)
Inukami (ecchi comedy)
Kiba
Tsubasa Chronicles
Utawarerumono (or people on 4chan call Underwater Ray Ramono)
Zegapain

Anime to avoid
Naruto Gap fillers
Me My I strawberry eggs
Blood movie
DBZ (any show where it takes them 5-10 eps just for 1 fight has problems)
Soul Link
Cluster Edge
Gasaraki (it was cool when they talked about their past lives but when it got to the modern time I kept falling asleep)
Vampire Princess Miyu tv
Alot of 1 shot movies tend to be horribly bad.
Anything Based on a video game is often horrible.