The "Old West" of The United States was an era that ran roughly from after the Civil War to the turn of the century. And those few years, from the 1860s to 1900, fall into a time frame that is described as late Victorian. Some people will argue that the Victorian era goes until the beginning of World War I, but for our purposes it ends with the death of Queen Victoria in 1901.
The late Victorian Era is a time of industrial revolution. That means steam engines, and other such mechanical marvels. And those mechanical marvels made things like getting decorative metal, for use on houses, for example, very cheap for the first time. And remember that all type was set in metal in those days, too. So Victorian typography explodes with fonts! No self-respecting newspaper ad would use less than a dozen of them. And yes, sans serif fonts were already being used before the twentieth century, too, although not nearly as much as they would be later on. So look at Victorian design - look at old newspapers from the late 1800s.
But there are some mistakes that you need to avoid. And from a typography point of view, they are as bad as having your cowboy wear a watch, or having an jet flying in the background. And the biggest mistake is - Helvetica.
Helvetica wasn't invented until 1957, and didn't come into common use until the sixties. So don't write "Saloon" in Helvetica.
Typography is part of the picture.