When the wildest gunslinger in the west is wanted dead, an underemployed ranch-hand sets out to capture him alive for the biggest cash reward.

If the gunslinger is wanted "dead", why there would be a bigger reward for him "alive"?
The usual is "dead or alive", same reward, I think.

I was thinking about this story, I believe an interesting inciting incident that would be: The gunslinger steals the lead characters beloved horse. Maybe the horse has sentimental value to the lead character. Now the ranch hand is determined to get the horse back at all cost. (Maybe he doesn't even care about the reward money, all he wants is the horse back)

Standing in the way of his goal would be a specific ruthless bounty hunter that keeps getting in the way because he believes the lead character is trying to steal his mark.

Then add a goal for the gunslinger. He must be in (This old west city) by a specific time. (Which is why he stole the horse)

Finally give the ranch hand one useful skill, His father was an expert tracker and he grew up learning how to track from him.

So now you have a three way duel. The Gunslinger must be in (Let's say Dodge City) in three days and needs the horse to get there. The lead character is determined to get his horse back, and the bounty hunter is determined to stop the lead character because he believes the lead is a rival bounty hunter and he is determined to kill the gunslinger who is wanted dead or alive.

Whew... just some thoughts.

Good luck with this!

Agreed with the above comments.

All I can add is that you've set your MC a challange, but havn't explained how he will overcome it. IS he a former gun-slinger himself? A former expert sniper? Give him some form of advantage to aid him in his task. This way you can set him on a collision course with a worthy adversary.