This is a fun thing to think about, even if it was rather impossible for them to be produced then.
Of course, David Lean, Mr. Epic (The Bridge on the River Kwai, Lawrence of Arabia, Doctor Zhivago) would be director. Here would be some of my casting choices. Of course, getting ALL these actors would be the most ridiculous casting ever, making for the most ludicrously all-star cast in history, and itself be too expensive, but allow me to fantasize!
Frodo - Tom Courtenay
Sam - Michael Caine
Merry - Roddy McDowell
Aragorn - Omar Sharif
Gandalf - Ralph Richardson
Legolas - Peter O'Toole
Gimli - Rod Steiger
Boromir - Charles Bronson
Gollum - Peter Lorre
Theoden - Laurence Olivier
Eomer - Sean Connery
Eowyn - Julie Christie
Elrond - Rex Harrison
Arwen - Audrey Hepburn
Galadriel - Ursula Andress
Denethor - Orson Welles
Saruman - Alec Guiness