As much as I like to think I'm a De Palma fan, I realized that I had only really scratched the surface of his filmography. So I decided to dig into his early films, the ones I never actually got around to - namely his "thrillers".
One thing immediately stands out when you watch a film that he both wrote and directed himself: they're so bizarre, but in the best possible way. They never stick to a specific storyline, theme or genre, often shifting all 3 of these things throughout the film. Though he didn't actually write The Fury himself, it certainly fits into this aesthetic. If you've never seen an early Brian De Palma thriller, I'd highly suggest you do so as soon as possible.
I'd have to say that Blow Out is probably my favorite. It's such an underrated masterpiece in the thriller genre, But Body Double would probably be his most "De Palma" film in this early area of his career. It's kind of nuts and amazing at the same time. In any case, any of these would be a good one to start with, because they're all well representative of the specific way he makes films, and it's safe to say that nobody has ever come close to displaying the mastery that he has, and nobody probably will.
Also of note, if you haven't yet watched the fascinating and highly entertaining documentary De Palma, I'd encourage you to do so immediately. It's literally 2 hours of De Palma talking about every single one of his films in order and it's awesome. A must watch for cinephiles. I've included the trailer below: