Will do! Which would you recommend for a, I suppose, first time watcher?
Psycho-Pass is pretty heavy, but it's kinda like a sci-fi police procedural with an overarching plot. It's great if you have a good tolerance for violence and general messed up stuff. Noragami is kinda like the flipside. It's a fairly innocuous shonen dramedy about spirits and gods in a contemporary setting. So, light fanservice, lots of jokes, and some drama towards the end. Pretty standard stuff.
I dunno if Durarara is really entry-level, but it's my favourite so obviously you should give it a try anyway. It can seem a little repetitive and tough to follow, but when it gets going it's a lot of fun.
Fate/Zero is also just a great fantasy story, but it has the same writer as Psycho-Pass so shit gets pretty grimdark. The anime tones down the original novels' violence a
lot, though. It's a prequel to Fate/stay night, but was written afterwards. I'm assuming you won't be itching to read through the 50+ hour FSN visual novel, so if you're going anime-only then watching FZ first is fine.
Mushishi, Samurai Flamenco, and Kill La Kill are all
really aggressively Japanese, all in their own different way. Mushishi is heavily steeped in folklore, (knowledge of which is optional but doesn't hurt) Samumenco is like a neverending torrent of tokusatsu jokes and references, and KLK is "that" kind of "really Japanese".