You might want to round out your Paul Newman thread with The Verdict,(1982) featuring a somewhat older Newman and James Mason in what I think was his last film, and then see Nobody’s Fool with Newman ten years older than in The Verdict.
Newman did Hud, another great film, in 1963 which predates Cool Hand Luke by four or five years.
If you want 60’s movies, the obvious ones to see are The Graduate from 1967 and Bonnie and Clyde from the same year. Another film of the same era that I enjoyed was Blow-up from England in 1966. I am always captivated when I watch Peter O’Toole in Lawrence of Arabia (1963)
There are tons and tons of great movies out there. Two from the 40’s are Casablanca and The Maltese Falcon, both with Bogart and shouldn’t be missed.
And for the 70’s you have to view a couple of Woody Allen films, such as Annie Hall and Sleeper.
I could go on and on, but I won’t
SRM