This is an extremely complex question made all the more difficult by (the usual disclaimer!!!) the West is the largest region in North America and everything could change according to place and decade. The West also tended to lean on the urban side of things - which runs against intuition because of all the movies about wide open spaces: the reason why they were wide open was because unlike the Midwest, those spaces couldn't support many people, so Westerners tended to be clustered into towns.

Because the West was a place filled with "instant" communities and societies, there could be considerable social/economic mobility - far more than in the East. The Irish, for example, did very well in the West. Even African Americans could find places where the chances of success could be greater for them than in the Eastern states. But your question runs along the lines of occupation rather than ethnicity, so let's focus on that.

The West did not have an established aristocratic class (like the East), but it very quickly did have extremely wealthy people: the "Gilded Age" was alive and well in the West. These tended to be investors who were lucky or successful at exploiting opportunities, and there was, indeed, a great deal of money to be made in the West. Let's put the "very wealthy" aside as a given and move on to understand the specific mechanics - the economic ladder as it was.

A skilled laborer could do very well in the West. In 1864, Comstock miners famously demanded (and received) an minimum of $4 per 8 hour shift for underground work - some made more than $4 depending on experience. Underground carpenters usually made $3.50. The $4 per day was a great wage: Colt in Hartford, Connecticut offered workers $1.25 per 12 hour shift in the late 1850s, and this was regarded as generous since neighboring canal diggers were making 75 cents a shift. All that said, prices in the West were often inflated.

Your sheriff making $250 a month seems way out of scale. I question that. One could hope to do better than one of those underground miners by being a merchant, but many business failed (as they do now) so the margin of success could be surprisingly narrow. And given the short life expectancy of a Western mining town, one could quickly lose a great deal of one's investment. Failure was always a possibility.

All this is nibbling around the edges of your question, however. Perhaps we are best to divide our imagined community into industry; support service businesses; and government. In labor, the more skill one had the more one made, and someone with skill in industry could do better than most people in the other two groups.

In the support service business, there could be a great deal of money to be made. If someone involved in banking or newspapers were able to capitalize on stock manipulation one could do very well (what would be illegal inside trading today was perfectly acceptable then). Mark Twain bragged to his family how he could make a great deal of money on the side as a reporter by writing pieces that would raise (or crash) stocks for a given mine - or attract trade to a given business: reporters often exploited the power of the pen to make a great deal of money. But there was also a lot of scarping by and a lot of failure for people in business. Sometimes, it must have seemed that luck was more important than skill or hard work. In general, those of the business support sector represented a wide spectrum of possibilities, ill defined by specific area of employment since anyone could succeed and anyone could fail at any of these businesses.

Government gave one an opportunity to exploit the stock market or any number of other "insider" business deals. Some did very well, but in general - and by salary, one did not ascend as far as one might in business - much like today.

There's a lot here to chew on. I'll leave it at that and answer - later - any specific questions.