The most used type of artillery used in Missouri during the civil war had to be the six pounder field gun. It was the most manufactured type of field cannon in US history. There are several models of a 6 pounder gun but the M1841 was the most built model. The M1841 was aprt of the 1841 program of artillery adapted for the army, the other models were actually developmental models finally arriving at the M1841 model. It was light enough for rapid movement, it could be manevered by hand as it was in the mexican war. It was available in large quantities, in all of its models.
The 12 pounder Mountain Howitzer was an ideal field gun for the actions in Missouri, Kansas and Arkansas but the problem was it was not available in large quantities.

My vote is the six pounder field gun and its M1841 model as the most used artillery in the fighting west of the Mississippi River.
Ron