Well, orathaic, I'd say that the liberty interests and democracy as a governing principle are set in opposition to the authoritarian monarchies rather than communism (although certainly applies there). Roughly it is the notion that personal liberty from the arbitrary application of government force applied for the benefit of the ruling elites is at the core. That gives one rights to security in ones home, possessions and privacy from government interference, as well as to speech and political activity, in order to have a civic society that can provide a check on ruling elites. Needless to say ruling elites often don't like this arrangement. As for human rights and civil rights, those movement come in response to efforts by ruling elites to suppress the political and social participation of others who might challenge them. Domestically, that translates into attempts to deal with institutional sexism and racism and the social bigotries that act to suppress in the individual freedoms of ALL members of societies. (Odd how conservatives love to mouth the words "freedom" and "liberty" but are the fastest to work to deny both to women, minorities and other groups who aren't white males. ) Similarly, the aims of human rights are grounded in similar values.
Naturally, these are aspirational values that we can't say America has ever done more than stand for partially, if only because only a fraction of the American people actually subscribe to them. The rest want authoritarianism as long as it benefits them and don't give a rats ass about the harms inflicted to others. The issue with deciding what America "stands for" is that America is divided about these core values, and only some people endorse them more than at a superficial level.
Thus, by the adage "don't tell me what you believe, show me what you do and I'll tell you what you believe" we are left with a US that is a traditional imperialist colonial power with a shading of decency added to the mix, but clearly a blend of two competing philosophies. The US is exceptional for its power and for its bizarre blend of enlightenment philosophies and conservative theocratic values. If you look at measures of social attitudes, you'll find that Americans sit all by themselves in a netherzone between the western democracies of Europe and traditional societies such as Saudi Arabia or Nigeria. We're unique in the sense that our actions and attitudes are of some hybrid chimera that never quite made it into the twentieth century.