Image has a ton great titles too. I never gave much thought to them until one day I realized how much space they take up on my shelves. Saga alone takes up a ton of that space, but other series I've enjoyed include The Wicked + The Divine, Monstress, Paper Girls, Skyward, and Injection (although I think that one has been canceled after the author was)
As someone unfamiliar with graphic novels, can you recommend some good ones that have more "adult" themes? I don't mean porn, but like storylines that are more interesting than bam bam pow pow. Maybe more like a typical novel than a comic aimed at younger readers, if that makes sense?
Transmetropolitan. Basically cross Hunter S Thompson and Futurama. The blackest of black comedies. Likely to be a love/hate kind of thing... but it's one of the books that opened my eyes to what a non-superhero comic could be.
I've only ever dabbled in caped heroes, so most (if not all) of what I listed is what you're looking for although Saga deserves special mention. I'd consider The Sandman (sadly DC) a must read. It takes a volume or two to really find its footing but none of it is bad. Something Is Killing the Children is good too.
There are comics to suit every literary taste. Understanding Comics, by Scott McCloud, is an examination of the medium in the form of a comic. Maus, by Art Spiegelman, is a dual memoir of holocaust survival and the creation of the book itself. Both are widely translated and available in public libraries.
You could use the Eisner Awards as a source of recommendations. Read the blurbs and preview pages of the winners and nominees, and select the book or series that appeals to you the most. For example, Ballad for Sophie was a recent highlight for me, and was nominated for four Eisner Awards.