Well, Samurai Champloo, Bebop, Escaflowne, Macross Plus and Wolf's Rain are all tied together in that writers/directors have worked on them. Yoko Kanno (the Composer) also worked on all of these, so I recommend them all.
I would say stay away from the Ghost In the Shell movies at first. They're re-writes from one of Anime's worst writers/directors Instead wwatch the TV series STAND ALONE COMPLEX and 2nd Gig, they are more true to the Ghost In The Shell epic.
TV series are generally much better than Movies. Ninja Scroll is lame, and Samurai X the OVA is excellent. Anyone who likes Dragon Ball Z, and those who have birthed it into this world should be shot. It's crap. Utter crap. X the movie is also crap compared to the Series.
There's very few shows that Adult Swim shows that are worth it. FMA is crap. All of the good shows are on WAY late at night, but for the most part they've been a big proponent of the Gundam series.
FLCL, Bebop, GITS, and Wolf's Rain re their best series, and most people wouldn't even know about these if they didn't watch Adult Swim. Being Otaku doesn't mean you have to be elitist, but that you keep an open mind and know that there is SO MUCH more out there that isn't shown on Adult Swim.
It all depends on what you like. Do you like Samurai? Do you like big robots or Mech? Do you like guns and hot chicks firing those guns? Do you like romance, or comedy, or horror? There's more Genres to Anime than there are American Film. Let me know what you like and I can suggest from there.