There is no objectively correct answer to this question. People from different political ideologies and different schools of international relations thought have different answers.
From the liberal/idealist perspective (this is an International Relations term, not referring to liberalism as a political ideology), American ideals should play a major role in setting our foreign policy. Idealists believe that spreading democracy will reduce the amount of conflict in the world. This is one reason why, for example, President George W. Bush wanted to invade Iraq. He believed that the US could bring about democracy in Iraq and thereby create an ally in an unstable region. He believed that democracy would spread from Iraq and eventually make the Middle East more peaceful.
From the realist perspective, American ideals should play no part in foreign policy. Foreign policy, in this view, is all about what makes our country more powerful and more secure. In this view, countries have a strong desire to remain secure. They can remain secure through military power. Therefore, we have to, above all else, maintain our military power. This is why, for example, we were willing to back terribly repressive regimes during the Cold War so long as they increased our power relative to that of the Soviet Union.
My own view is a mix of these. We surely need to be realistic to some degree in foreign policy. However, it does seem likely that we will be better liked in the world (and therefore more secure) if we act according to our ideals as much as possible.