There's only one way I can list my three favorites:
1) John Wayne westerns
2) Clint Eastwood westerns (except for Beguiled)
3) Robert Duvall westerns (Open Range, Lonesome Dove)
There are a couple of movies with Tommy Lee Jones that aren't exactly westerns, but where he plays a sheriff or Texas type character (and he is a genuine, native born Texan): No Country for Old Men, The Three Burials of Melquiades Estrada, and of course he was excellent in Lonesome Dove. (He did a great comic turn in Man of the House, as a Texas Ranger protecting a sorority of college girls - tough duty that!)
Then there are many runners-up, that I can't categorize by an actor, but a few are:
Tombstone/Wyatt Earp, The Wild Bunch, The Professionals, Dances with Wolves, Tom Horn, and The Magnificent Seven.