My own Coen Bros. favorites list, from the top, would be The Big Lebowski, No Country for Old Men, Fargo, A Serious Man, Raising Arizona and Inside Llewyn Davis. I hated, to varying degrees, The Hudsucker Proxy, The Man Who Wasn’t There, Hail, Caesar! and Barton Fink. The rest I either haven’t seen or don’t particularly care for.
You’ll definitely want to read the hilarious autobio Barry Sonnenfeld, Call Your Mother. The director got his first break in Hollywood as the Coen Brothers’ cinematographer, and he has some great stories about filming Blood Simple.
I love What’s Up, Doc! Very, very funny - one of my all-time favorite comedies. And at least four of the cast were also in Paper Moon, another favorite Bogdanovich movie for me.