Just a small nit to pick over "They were a small band of men, largely untrained and in the beginning, without real leadership."
All of the colonies had local militias, and they mustered for training and drill regularly. There were fines for failing to show up, and for failing to secure the listed equipment within the listed time period. This held true across all of the colonies. They campaigned against the Indians, the French, and the Spanish, as well as, in some cases, pirates.
The local militia was of company size (perhaps 100 men). They were not trained or experienced in set-piece battles where regiments or divisions or entire armies faced off against each other. But they got training pretty much as soon as they could all be assembled into what you could call an army.
None of this is meant to take away from the rest of your post. My intent is, rather, to highlight that those who fought for freedom from oppression and tyranny were willing to go up against considerable odds, and were generally sucessful in spite of the difference in strength and supporting arms.
As for when, where and why we send our troops - the exercise of military might is merely the ultimate exercise of diplomacy where talk has failed to win your position. Go tell our elected representatives how you want to exercise diplomacy.