I was a Reserve Deputy for 15 years. I carried a S&W 610 loaded with Full House 10mm ammo. I had a custom Quad Moon Clip Carrier in Black Basket Weave on my duty belt.
As a rural Deputy most Gun Play will be shooting livestock, and deer hit by vehicles. In Kraigways area you can probably add moose, elk, and antelope to the list.
If you ask any old salty Game Warden what he would like to carry for a handgun, most would pick a revolver in 357, 41, or 44 magnum. The reason most semi auto pop guns do not have enough sudds to finish off large animals that are injured quickly with a single shot.
Next issue is the one well aimed shot. I have always shot revolvers more accurately. Probably a combination of better sights in the first place, and a more accurate platform.
I would probably go with the Marlin 30-30 for my saddle rifle myself. Like was said above the flat side lever action carrys well on a horse. In Wyoming that makes very good since.
Talk about a different world to work in. A city officer would never believe you can rack up over 300 miles on an 8 hour shift, and stay in one County. How can this happen? By being the only Deputy on duty in a 1000+ Sq Mile County on a Sunday. Some times Sundays are not just for catching up on reports in the office.
Bob