This will sound crazy but I've never seen anime. Now I'm curious about it, what would be a good one to start watching, preferably something for adults?
Chocolate is totally on the right track. Just like with movies or other media, genre is also very important. Some popular ones you might see pop up would be Monster, Akira, and maybe Legend of Galactic Heroes (an oldie but a goodie). That is taking into consideration anime targeted at a more mature audiences. There is actual a fantastic mystery anime currently airing under the name Boku Dake ga Inai Machi (The town where only I am missing). It is fantastic. I highly recommend it.
But don't let labels turn you away! One of my personal favorites, Tonari no Kanbitsu-kun (My Little Mosnter) has a primary audience of young adults of the female variant. Nevertheless, good quality will be good quality!
As for that list you mentioned chocolate, I'll grab it when I get home this evening. But it's a bit more general but always a nice place to start.
Edit: Looks like I have it on my laptop
And one last thing, and this is
very very very important! Japanese media has a lot more freedom on what is "accepted" compared to western media, on average. So in watching some shows targeted at adult audiences, you may notice some things that we may consider borderline, but by their standards is perfectly acceptable.