Many guns have a western feel, I think that the Winchester 94 has it the most. While it didn't see a lot of use in the winning of the west, it was one of the most popular guns right from its inception, and was used at the end of the west until the whole country was settled, right up until today. It was all the rage when the hot new cartridges (30-30 and 25-35) came out in 1895, and of course it had plenty of followers in it's original 2 "old reliable" cartridges, the 32-40 and 38-55. It's light and fast handling. It digests dirt and dust pretty well and is easily maintained on the trial.
The Marlin 1894 has a good amount of western feel too, this one being a Cowboy Limited model with 24" barrel chambered in 357 Magnum caliber. The original 1894s saw service in the west in limited numbers before it was officially closed, but like the Wincehster 94, remained a trusted companion as civilization crept into all the small towns and overtook the remaining wilderness.
The Winchester 92 sure feels western, but only if you drop the safety and convert it to half cock notch, like this Turnbull finished version. The 92 does have a lot of western appeal, and having a takedown version brings visions of riding on a train to reach the west.
The same that can be said about the 92 applies for newly made 1886 Winchesters, they just don't feel right with rebounding hammer and tang safeties. But chambered in 45-70, they do have a lot to offer, history wise.
I think that the gun is only half the equation, but the caliber is important too. A caliber with history is always interesting to me. 357 Magnum has plenty of it, and occasionally you find original 1892 rifles that have been converted to the caliber. This is interesting in its own right because ranchers and cowboys have always had an affinity for custom guns, and many were sent to the west and have been made since. I'd love to find an original with a long-ago 357 conversion.
I guess my vote goes for the Winchester 94 in 30-30 first, and second choice for the Marlin 1894 in 357 Magnum.