I recommend Cowboy Bebop as a compromise - still human and a little tragic, but it has all the emotions instead of one!
Oh, but Evangelion has more than one emotion! True, it's mostly despair, but that's not the only feeling! There's also dread, revulsion, anger...
In all seriousness, though, Cowboy Bebop doesn't sound like something I'd be able to get into easily. I prefer my shows to at least
start plot-driven, to give me something to latch onto before I get used to the characters. I'm not saying it's bad, just not necessarily my cup of tea.
I've been meaning to give Monster a shot, and I don't get triggered easily, so I'll certainly watch it at some point. Not right now, though.