Good call on Maverick, that is a truly fun movie, very 90's, everything that was great about that era, huge budget, elaborate set pieces, and big name actors having fun, and tossing off one liners at a rapid pace.
If you want to go way back, Red River from 1948, with John Wayne and Montogomery Cliff, is probably one of one the most iconic westerns of all time. Yes, The Searchers too, even if it is belabored, and too long. The less serious ones like Rio Bravo and El Dorado, are classic John Wayne westerns, they are basically the same movie.
I watched a lot when I was a kid, some I was too young to appreciate, possibly, like High Noon, with Cary Cooper.