So, I'm going to be honest. I haven't watched any of those films. Despite being a big fan. My ex wife once bought me a DVD collection (when that was still a thing) of their earlier films (most of which you mentioned), and one of our dogs chewed them up! Lol. So I've never watched. What would you recommend as a start, for their older films?
And have you watched Intolerable Cruelty?
I have watched Intolerable Cruelty. To be honest, I have a bit of a soft spot for George Clooney (please do not repeat this, LOL) and I like the chemistry between him and Jolie, but it's also a flawed film and I didn't like it that much second time around. So I'd say, pretty good, with potential to be really good at times.
As for what are the best movies, it depends on what you want. Miller's Crossing is a gangster film, noirish, suspenseful. It's great. It does gangster with a bit of a lighter touch than Godfather films and the like. Not a super light touch, but it's not "leave the gun, take the cannoli." It's got wonderful performances; a strong plot; and plenty of suspense.
Barton Fink is more of an art film. Amazing performances -- including by John Goodman, in maybe his best overall performance -- and there's a lot going on. It's one of my favorites, though it's not necessarily for everyone. It's about a high culture playwright from NYC, who ostensibly was writing a theater for the common man but in reality he was a darling of the art scene there and never interacted with the "common man" too much. So they hire him to go out to Hollywood and task him with writing a B wrestling film. Turns out that the "common man" is a bit more elusive. Barton himself is obviously modeled on some of the playwrights of that era (Eugene O'Niell comes to mind), and there's a very interesting send-up of Faulkner (who did himself go to Hollywood late in life, where he found little success as a screenwriter). It's a great movie, but not necessarily the most approachable.
Blood Simple is a noir thriller that gets some acclaim in various circles. I was not that impressed. It's fine. It's competent. It's fun to watch. But compared to the other films, it's meh.
Hudsucker Proxy is their first serious attempt at comedy, in my view. Much of the humor in Fargo is just funny accents, which is amusing but shallow. It's bit of a weird film, and it's not for everyone. I like it. Don't love it. The best 45, 50 minutes are amazing, but it's inconsistent.
I sort of lost interest in them after Big Lebowski. I'm not sure exactly why. I guess their movies just didn't appeal to me. I saw the black and white one that followed Lebowski and found it boring. No Country is an exception, of course, as I like that film. It wasn't as if I was consciously avoiding them. It was just like, my interests were elsewhere. I didn't like Burn After Reading too much.