I just got off watching an introductory Dredd video on a youtube channel called something like "Past Midnight", they recommended a series called America, which I haven't read, but it's supposed to be a good primer for the comic universe. Though Dredd is, in fact, barely in it.
I doubt the Case Files have reached Origins yet, but that's worth a look, it shows how the Judge system began, and is also one of the occasional "cursed Earth trek" stories, with weird mutants and crazy townships.
One word of warning, while a lot of the arcs that have since been published as books are standalone, they often have lead-in stories that may have occurred years before. Origins features the New Mutant Army, which first showed up in a story from several years previously, in the Megazine. The recent Day of Chaos epic revealed that Mega City One's mayor was a wanted serial killer, how did he reach that position? A Megazine story fron several years prior has the answer!
It's still nowhere near as bad as capeshit, though. After a while the insanity of Dredd's world just kind of washes over you. If you don't know exactly how a serial killer became mayor, it doesn't really matter, you just accept it as "yeah, that's something that would probably happen".