This study looked at gun ownership in Probate (death) records... It seems that around 1774, ~50% of estates listed a firearm while only ~30% listed any cash... Although I'm going to guess that probate records are going to favor the wealthier citizens... I know this is 100 years before what you are looking for, but it's still a good place to start

http://scholarship.law.wm.edu/cgi/viewcontent.cgi?article=1489&context=wmlr

It really depends who you ask. Statistics are hard to come by. Often, we turn to statistics about gun violence to try to determine how widespread their use was, which is itself problematic: only a tiny fraction of gun owners have to use their weapons against people. Some historians have challenged the claim that the West was a very violent place where gun ownership was very widespread and violence could break out at any time. They point to the fact that some cities had less than one murder a month by firearms, and it's certainly true that the myth of gunfights in the West had already been formed by imaginative newspaper accounts and popular literature by the 1890's. Other historians point to crime statistics, particularly those with high levels of tension, that suggest gun violence was quite common.

The Colt 1851 Navy, Colt Army 1860, and Colt Single Action Army all sold more than 200,000 models, though these were also exported and used by the military. Two of those models were obsolete by the 1890's, but it gives you an idea of just how many of these guns there were.

According to William Kelleher's Violence in Lincoln County, 1869-1881: A New Mexico Item, while the revolver enjoyed considerable success in the East, it only started gaining popularity in the Old West in the 1870's. If you were living in the West, where you did much of your hunting yourself, you wanted a gun you could use for more than self-defense. Therefore, rifles and shotguns were predominant. This had changed by the 1890's. Kelleher mentions that the availability of alcohol and guns (especially in combination) led to high levels of gun violence in the West. By the 1880's, the price of the revolver had dropped to around two dollars for an affordable model. The wage of many workers was a dollar a day, making them both available and affordable.

By the 1890's, many efforts to bring stability and control to the West were being made. Many towns banned carrying firearms within city limits ("wild" towns like Tombstone among them). As pointed out by Clare McKanna:

In 1889, the Arizona Territorial Legislature passed a bill that prohibited the carrying of pistols and other weapons "within any settlement, town, village, or city within" Arizona Territory. Further, saloon keepers were required to post signs requiring armed men to give up their weapons upon entering the saloon. The fine could be from 25 to 100 dollars and forfeiture of the weapon upon conviction.

McKanna's article, "Alcohol, Handguns, and Homicide in the American West: A Tale of Three Counties, 1880-1920," looks at three troubled counties in Colorado, Nebraska, and Arizona where gun violence was common. He finds that handguns accounted for between 58% and 70% of the murders in those counties. He blames alcohol, racial and ethnic tensions, and the culture of vendettas. He mentions that in one city,

Prosecutors convicted only 14 percent of those defendants accused of homicide in 21 vendetta cases. Because these were blood feuds, prospective witnesses refused to provide information on possible suspects for two reasons. First, it was an unwritten code of the vendetta that you allow the aggrieved family to settle the killing. Second, to implicate someone might draw your family into the feud.

Unfortunately, McKanna's article several times mentions that handguns were common and easily purchased in the West, but doesn't provide backing for these claims or go into detail about the statistics of handgun ownership. Some reviewers have pointed out that McKanna's claims that gun violence was much more common that previously thought can't be deduced from picking out three particularly combustible regions and then using their data to generalize about the whole region.

Here's an interesting primary source from 1890 that addresses the issue of handgun ownership:

Overland Monthly and Out West Magazine

Volume 16, Issue: 91, July 1890

James O'Meara "Concealed Weapons and Crimes"

In this editorial O'Meara (1825-1903), a San Fransciso journalist, editorializes on the impact of revolvers as concealed weapons, which he viewed as an increasing problem after the Mexican War and a major challenge to order in San Francisco in 1890. He notes in particular that "In European nations revolvers are not so common, nor so cheap, as in America."

He is obviously pushing an agenda (support for law enforcement in San Francisco) but the piece offers an interesting view of the role of handguns in Western urban crime in the period in question.

Supplemental questions, how much was a handgun in those days? How many days work would that represent for a low end worker at the time?

Chronicler of the Old West, newspaperman Owen P. White (Autobiography of a Durable Sinner) covered this question. Knife fights were much more common than gun fights. Everyone carried a knife, a multitasker. Hand guns were heavy, easily fouled, etc. Rifles, another mulitasker, were ubiquitous.