Yes, NGE is a bit polarizing. No, that doesn't mean you shouldn't at least try to watch it. It has die hard fans for a reason and liking it is all really down to opinion. Either way, it was a very influential show and fairly important to the history of the medium. Some would say without NGE, you wouldn't get Code Geass. Also watch End of Evangelion. There's a lot of nonsense(when people say "you don't get it." rest assured they don't either, I don't think anyone does and Anno is being dead silent on that front), but it's damned entertaining. If it's the fanservice people swear is in it that keeps you away, I promise you, most of it either isn't or is damned unsettling when you actually think about it. The dub? Well a lot of people are annoyed by Shinji, but he's supposed to be a whiny ***** sometimes, just like a regular 14 year old. I'd argue the dub is worth it for one reason, the voice of Asuka, a girl raised in Germany in the story, actually speaks beautiful German.
I favor Spice and Wolf. It's relatively light in tone(dark is not mature, High School of the Dead taught me that), but it takes quite a mature stance on relationships and most of the tension and drama is centered around medieval economics... Can't really make that exciting, but it's really not as bad as it sounds. Also, if you loved Moxxie's voice from Borderlands, you'll love the dub and the chance to hear 26 episodes of that voice. Also fairly light on fanservice once the main heroine gets clothed. Though she is a teasing flirt, that's half the fun.
Black Lagoon... really depends on what your definition of mature is. Lot's of blood and violence in the style of a 90's era action movie(that the series intentionally parodies)? That being said, it's an interesting show to watch for one main reason, the main characters(Revy and Rock) actually change somewhat through the course of the show. Static characters can be alright, but it's a better story when they actually change their outlook somewhat. There's a fair bit of fanservice, but I never found it to get in the way of the actual events happening like it did in High School of the Dead. The dub is alright, nothing blatantly bad.
I'd say D.Grey Man if not for the fanservice(though generally aimed at women, bizarrely enough, excusing Lenalee's perfect and oft shown legs) and tone whiplash that permeates the series thus far. The characters are generally quite decent and the world doesn't really get more crappy, which normally means mature show, but there's a lot of silly in there too. Granted, this is when I'm only like 10 episodes into a 100 episode show, but hey, call it a first impression.