It also really depends on where your characters are. If they are in, say, rural Pennsylvania then violence is going to be relatively rare. If they are in a mining boomtown in the west, then there is going to be more of it. It's interesting to note that there wasn't nearly as much violence as we have been brought to believe there was in the old west. While it was there, no question, it wasn't quite the daily shoot-out in the street movies and TV would lead you to believe. Places like Dodge City, Wichita, Deadwood etc were indeed violent places for a time, but eventually the decent citizens of the cities would get together and either hire "good" law enforcement (who weren't always as good as one might hope) or would band together in vigilance committees and hang a few miscreants. Nobody wants to have bullets flying around the streets their kids play on.
Probably the best cinema representation of a genuine old west gunfight is Kevin Costner's "Open Range". Everybody shooting, mostly missing, clouds of smoke obscuring everything, people getting wounded multiple times and living (guns, especially pistols back then, were not exactly death rays. Given the state of medicine at the time you might die a few days later, but you'd still be ambulatory for a while after being shot), people losing their nerve and running away, all of this is authentic and based on real things. Also authentic and still valid today, when the bullets start flying, the townspeople just get their heads down and try and stay out of the line of fire (For the most part...it's a movie, after all). But it's mostly confusion, smoke, noise, people running around, reloading (it takes forever to reload a Colt SAA in combat), etc.