My recommendation for first creator-owned Brubaker book is The Last of the Innocent
I didn't take to Criminal at first because I was thinking "this is just straight-forward crime stuff, and I don't have a hard-on for crime, so I might not be the audience for this".
I do like crime, but I like Raymond Chandler novels, and the movies of the Coens and Shane Black, because that stuff is really goddamn funny. The early Brubaker stuff I tried, by comparison, is mostly played straight.
But The Last of the Innocent is where I came back, and that's where he got a little more creative with what he was doing. That isn't just some plain-ass crime story, it's a fun use of the medium that really wouldn't work at all if it wasn't a comic book.
From that, I went to Fatale, and that was another departure from what I thought of as an archetypical Brubaker comic. Now that I've seen more of his range, I've come back around and become more open to the straighter stuff too.
The Fade Out is really damn good. The thing I liked most about it is that while it's a mystery, it has no interest in obfuscating facts or tricking the reader or trying to pull out some shocking twists for shock's sake. You can and will get ahead of the story and be able to figure it out, because it's a logical, plausible story that feels like a real thing that happened, involving real people with real motivations, so it all comes off feeling authentic and honest in a way that I don't think enough mysteries do.
This post went on longer than I intended. Sorry.