With Akira, I remember being freaked out seeing it as a kid on cable, but at this point I barely remember anything about it, so its hard to say either way.
If you want to get into anime, you watch Cowboy Bebop, since its distinctly riffing on Western genres and tropes, it's probably one of the most accessible out there (and genuinely awesome throughout). I'd also recommend Grave of the Fireflies, which is a completely straight-ahead war film that just happens to be animated (and is unflinching and bleak as hell).
But ya, I also have a tough time with anime, because the cultural sensibilities and writing just make most of it impossible to get into at all.