Posted 10 October 2013 - 10:22 PM
I've tried to pick good "gateway" drugs as oppose to something with specialized tastes
Slayers franchise: easily accessible, a hybrid comedy/action, reasonable romance pacing, and well known for first thrusting a single competent female lead into the spotlight, as oppose to a female team or a male. The once amazing action scenes are likely not to impress due to age, but given the other shows you've watched, I suspect it'll be fine. NEXT and TRY are the best of the 5 seasons by far. NEXT is generally considered a classic.
Haruhi Suzumiya series: Lovingly animated, fun story, and probably the closest thing to "what the hell genre is that" that I can remember for a while.
Martian Successor Nadesico: Not great on the animation, but the really beats the hell out of most Gundam shows in my opinion. Questions morals way better, is a hybrid comedy/drama series, and has the best plot device ever: anime. It's not really a mecha series since mechs play so little in screen time. More of a space opera (space drama).
Psycho-pass: Probably the only new show I'll recommend. Probably because it's the only new show I've seen in ages. It's a good show with an interesting tone. And generally tries to deliver fan service a well deserved kick in the crotch.