I haven't watched anime in around 8 years which was when I was watching stuff like Naruto and Bleach. Recently, however, I decided to see if Cowboy Bebop was any good and I ended up loving it. In part, perhaps, because it isn't that much like an anime. Many of the things that I can't stand about the medium are absent from it, making it feel more western.
Now I'm willing to give some other anime a chance. I prefer story-focused as opposed to action-focused stuff, with good characters that you can grow attached to, but nothing melodramatic and nothing for kids. Bebop hit a good balance on this front. I much prefer the mystery/neo-noir/cyberpunk-theme over the samurai stuff, but that isn't necessary.
Any help is appreciated.