I recently finished watching flcl for the first time and I liked it a lot. enough to want to watch some more anime in my spare time maybe.
I haven't watched much anime, because I always assumed it was all either kiddy shit or perverted or both, in that weird-*** japan way. I want something that is either very stylistically interesting, or deals in mature themes (ie. not kiddy shit or perversion), or both.
here's what I have watched/enjoyed, so you have something to base recommendations on: Cowboy Bebop, Paprika, Princess Mononoke, FLCL, the first Ghost in the Shell movie, Akira, Bartender.