I dunno about anime series (I've seen a lot but not enough to determine which is the best) but for anime films I really like Howl's Moving Castle from Studio Ghibli and either Summer Wars or The Girl Who Leapt Through Time!!
Naruto for story Another for dayumness DBZ because it's DBZ obvs Pokemon yu gi oh and bleyblade because memories You can't ask an otaku to chose one it's just too hard
It's hard to list just one. But here is a list of my favourite anime: One Piece - It's a HUGE surprise that no one has mentioned it until now Naruto - The storyline, and I'm into fantasy/supernatural stuff Log Horizon - Again, storyline and fantasy Detective Conan - Story, and I'm into crime solving Those are the ones I could think of from the top of my head
Fruits basket is an old favourite that never gets old! And Barakamon! I wouldn't say they have the best plot or something but they're things that you can always go back to to have a laugh.
As for best plots twists I think I'll hand it to Code Geass. I can't say best overall because I love them all #crii