More than one is okay, as I know Western Expansion didn't happen overnight.
In the early 1800s through until after the Civil War, most Western weapons were loaded with loose powder and ball, rather than with self contained cartridges.
In the Mexican American War, the US army used a .54 caliber rifle and a .69 caliber musket.
Colt percussion revolvers also were loaded with loose powder and ball and came in various calibers.
After the civil war, self contained cartridges became popular.
The most important cartridges or ammo sizes in the American West would include.
The Sharps rifle, used as the main buffalo gun to hunt the buffalo off the plains, generally in .50 caliber. The US Cavalry also used the Sharps in carbine form as its main weapon post civil war. This was also in .50 cal.
The 1866 Winchester lever action used the .44 Henry rimfire cartridge.
The 1873 Winchester (probably the main rifle used in the West) most often used the .44-40 centerfire cartridge.
This was the same cartridge used in the popular Colt "Frontier" revolver, and it was useful to have a common cartridge for rifle and pistol.
The .44-40 centerfire may have been the most popular cartridge on the Western Frontier.
The Colt "Peacemaker" most often used a .45 cartridge.
The Smith and Wesson Model 3 often used the .38-44, while the "Russian" and "Schofield" Smith and Wesson revolvers both used a .44 cartridge (though the cartridges were different and not interchangeable).
The Winchester 1876 was built to use more powerful cartridges than the 1873 (rather than the pistol cartridges which the 1873 used). It was often chambered for .44-75, .40-60, .45-60, .50-95, and .45-75 (as used by the Canadian Northwest Mounted Police).
The cartridge that "won the West", though was probably the .44-40 centerfire. The Winchester 1873 and the Colt Frontier revolver were a possibly the biggest selling guns on the frontier, and they both usefully used the same cartridge.
Sources:
http://en.wikipedia.org/wiki/Smith_%26_Wesson_No._3_Revolver
http://en.wikipedia.org/wiki/Smith_%26_Wesson
http://en.wikipedia.org/wiki/Winchester_rifle
Can you expound on that a bit? Namely, as you say the Westward Expansion didn't happen all at once. When you say cartridge, I assume you mean metalic cartridges, and are looking around Civil War to post Civil War era?