Here's my ordering. My definitions of the moral foundations are informed by referencing
http://moralfoundations.org.
1. CareI see care as the virtue that all other virtues exist to serve.
2. Proportionality/FairnessThis is important to me. One person shouldn't be treated better or worse than another person for nonsense reasons. Those who harm others ought to face justice; it's not pleasant, but it's what they deserve. I side with care more than fairness because I'd rather see a malefactor redeemed than destroyed.
3. LibertyThis one ranks close to proportionality/fairness for me. I see the two as aligned because freedom to act is most meaningful when it is tied to responsibility to accept the fully-understood consequences of the action. And yet, the two are in tension because our world doesn't mete out consequences justly or predictably. Some who work hard remain poor. Some are rich due to privilege rather than merit or effort. But I wouldn't call for correcting circumstantial unfairness through excessive taxation or other heavy-handed measures, because I see freedom to struggle, to earn through one's own efforts, to voluntarily give, etc. as a virtue in itself. I'd like to see the world made more just in a way that treads lightly on personal liberty.
4. SanctityFair warning: my opinion here is going to tick some people off. There are some things (porn, casual sex, recreational drug use, etc.) that I see as harmful to the human psyche and to society at large, even though other people will explain them away as harmless when done safely. This ranks below liberty for me because I recognize that people are free to do what they want as long as they're not harming others. On that same token, I'm free to explain why I think those things are a bad idea. And others are free to listen, or not.
5. AuthorityI appreciate the merit of following leadership and laws, so that things run smoothly, work gets done, and people don't accidentally run into each other and get hurt. I'm aware of the danger of committing cruel, unjust, or oppressive acts in the name of obedience. As such, I hold leaders to high standards, and I have the most respect for leaders and laws that hold up morally when rigorously questioned.
6. LoyaltyI'm wary of the dark side of loyalty, where "If you're my friend, you'll hate all the same people I hate. You'll join me in throwing our rivals under the bus." That strikes me as ugly. But loyalty does have its place. I recognize the need make sure that my family is safe and well-cared-for before I reach out to care for strangers. I don't think I value the lives of my own race or nationality above those of other human beings around the world; in any case, I strive to have compassion for everyone. I suppose my loyalty is to the human family; I see them as more deserving of human care than any other species is.
Whoever mentioned Truth as a possible moral foundation, that's a good call. Truth is important enough to me that I'm relieved that I didn't have to rank it with the others.