If you grew up in Montana, you basically had to read A.B. Guthrie, Jr. His “Big Sky” series is six books, but the best are the first two, The Big Sky and The Way West; he won the Pulitzer Prize for the latter in 1950. The books are stand-alone, though they feature some of the same characters, so you could just get The Way West if you wanted.
For more of a sampling of western literature I would recommend The Best of the West: An Anthology of Classic Writing from the American West, edited by Tony Hillerman. It’s fun, but kind of hit or miss (as many anthologies are).
For the Native American perspective, I would recommend Fools Crow, by James Welch, which tells the story of life among the Blackfeet in the mid-nineteenth century. It’s a great book, but does not end happily.
And, of course, though it’s not really “wild west” western, Undaunted Courage by Stephen E. Ambrose is awesome. (It’s about the Lewis & Clark expedition.)
Except for [Undaunted Courage, these are all fiction. I don’t know of a good all-encompassing nonfiction history book to recommend. “The West” from, say, 1750 to 1900 is a lot of territory to cover – literally. I think any book that tried to cover the whole thing would suffer from the defects of all “overview” history books: not enough detail; too little about too much. Do you want to know about the land rush, or the gold rush? Life for the Anglo “pioneers” or for the Indians, or the Chinese? Life in the saloons of San Francisco or in the soddies of the Dakotas? The Molly Maquires in the Idaho mines, or the vigilantes in Virginia City? Do you want to know about the “soiled doves” of Butte, plying the world’s oldest profession, or about the Buffalo Soldiers, black civil war veterans who helped explore the west?
For the real “flavor” of history, I think fiction is your best bet, surprisingly. But I will also confess that I don’t consider books about Missouri, Kansas, or Illinois to be books about the west, wild or otherwise. 