Well, if you like violent start with The Wild Bunch, Ride the High Country, The Ballad of Cable Hogue and anything else from the glory days of Peckinpah.
You have to watch Tombstone, Unforgiven and pretty much any of Eastwoods stuff from the 60s and 70s. Man with No Name Trilogy, Outlaw Josey Wales, Pale Rider, High Plains Drifter and Hang 'Em High. Toss in True Grit, 3:10 to Yuma, Django Unchained, The Hateful Eight, Butch Cassidy and the Sundance Kid. For genre mashups, Paint Your Wagon, the Ballad of Buster Scruggs and Cowboys and Aliens, A Million Ways to Die in the West, Blazing Saddles. You can stretch a little to include things like Tremors or From Dusk Till Dawn, while not technically westerns they're good monster/horror flicks in a western setting.
That should keep you busy for a while.