>>344151Sands of Iwo Jima, The Quiet Man, and all of the famous westerns he was in, except Rio Bravo, Liberty Valance, and True Grit (I dislike the excess and decadence of American westerns from the very late 50s and into the 60s, so I've been putting off watching those). Iwo Jima is the only one that wasn't directed either by Hawks or Ford.
The Searchers is one people namedrop to death, but it probably is the best Wayne film to start with if you're used to more modern movies. It looks great and has an interesting story, even if some of the acting can feel a little hokey.