The first anime I saw was Paranoia Agent and it was weird as fuck. Evangelion was second though and became my favorite. I am currently enjoying the new Rebuild of Evangelion movie series because it can almost be seen as a sequel as well as a remake if you pay attention to subtle clues.
One Piece is about pirates and that's why I love it even if they aren't traditional pirates. If you do watch it dubbed though watch the Funimation version. 4Kids dubbed it back in the '90s and made it more "kid-friendly" which means they ruined it. If you watch it subbed I think there are over 400 episodes and dubbed is up to 200 now.
Black Lagoon is about a group of mercenaries.
Trigun is hard to explain. It's like a post-apocalyptic futuristic old west anime with a big twist.
ME: 23 year old slightly bi-curious male. B: 19 year old bi female and my wife