I believe this may be addressed in the FAQ, but I will help where I can. The carrying of a firearm was often a necessity on the American frontier, especially while traveling the wilderness. However, the most common firearm would be a rifle, specifically repeaters such as the famous '73 Winchester. The repeater offered a high ammo capacity in the same calibers as revolvers of the day with extended range due to the longer barrel. The revolver was a popular sidearm for much of the same reasons pistols are today: compact, portable, and easily concealed. In addition to law enforcement and criminals, the revolver offered the cowboy the added advantage of retaining his weapon should he be thrown from his horse.

The issue of how many people at anyone time were packing is a complicated answer that historians better than myself have struggled to answer. Out in the wild you would find most people to be armed with a rifle or shotgun. The problem is that as transportation options such as stage coaches and trains reach more places the need for weapons while traveling decreased. Also, most towns required individuals to check their guns in and leave them with the local authorities. Most of the famous places we think of in the old west had these gun laws ( Dodge, Tombstone, etc). Most "big" cities in the old west made a substantial profit from liquor and/or gambling. Firearms do not mix well with either of those.

So short answer to your question: yes firearms were frequently used during this time period. Location and population numbers of a location could cause huge variables.

I teach American history and am a lifelong student of the old west. I am currently in my classroom so I do not have all of my personal sources with me but Guns of the American West by Dennis Adler is one of my personal favorites and may be of further use to you. He covers the variety of firearms from the period and even discusses the pricing options available as well as the numbers that were sold in several examples.