something where the anime departed from the manga and went off in it's own direction.
Mahou Sensei Negima Not for the better, really. But I would recommend the manga.
This also seems to be the case for Trigun, but I can't vouch for that because I've only watched the anime.
been informed by a friend to read Berserk, which I plan on doing
Try watching the Berserk series/movies first. I feel the series provides a better emotional attachment, but the movies are really wonderful once you get used to the art. Either ways, it'll give you some good grounding for your interest in the series.
Personally, I'm a fan of the 'delinquent' genre. Probably the most famous, and one that was translated to anime (not much branching off, however), is Great Teacher Onizuka. For the really good stuff that hasn't been translated, there's a few all with the same art style. Crows, which is followed by Worst, and then Drop where the main character is influenced by those mangas. Drop hasn't been translated past Vol 4 however (it's a dead project).
To continue that, but a bit further away in the genre, and with lower quality art: You've got ocha ni gosu(Dead project, but late into it.). Angel Densetsu. And Kyou Kare Ore Wa!(Anime adaptation).
To branch off into the 'delinquent rom-com' category: Midori no Hibi. Yankee-Kun to Megane-Chan.
Completely outside of the delinquent genre, I'm going to give two very enthusiastic suggestions:
I Am A Hero (Ongoing)
I Am A Hero is probably the best zombie manga bar none. Some people might choose the flashier, younger Apocalypse no Toride, but the themes and emotions that go into I Am A Hero completely eclipse it, almost by painful amounts.
Oyasumi Punpun can be described well enough in the MAL reviews. It's honestly a great look at depression and other emotions that aren't usually displayed successfully in media.
My MAL, in case you wanted to see my own personal ratings for these.