How does the government determine what type of farm to subsidize?
As with most things the government does, this decision is made on the basis of politics. Those types of farms which have enough political power tend to get subsidized.
In America today, farms do not tend to get subsidized based on how important the particular kind of crop they grow is for the United States. Instead, they get subsidized based on how effectively they can push Congress to subsidize them. This depends largely on how thoroughly a given type of farming dominates the economy of a state. The more it dominates a state's economy, the more that state pushes for subsidies in Congress.
Thus, this decision which should be made on the basis of economics is more generally made on the basis of politics.