In Sophocles' Antigone, which of the following would be the most important principle(s) to Creon and Antigone?1. loyalty or obligation to family...

Antigone and Creon believe in principles which result in a unbridgeable gulf.

Antigone embraces loyalty or obligation to family and observance of religious law as important to her identity. These principles are the basis of her convictions. Antigone disagrees with Creon's orders forbidding proper burial of Polynices’ body.  One reason is out of obligation to her brother.  In countering Ismene's objections, Antigone says "False to him I will never be found."  Antigone cannot envision a world where she turns her back on her brother. Demonstrating the need to honor her brother with a proper burial is part of that loyalty.  In her discussion with Ismene, Antigone also suggests that she must bury Polynices because it honors the gods' will.  Doing so would make her "sinless"; and if Ismene refuses to help, she will be "guilty of dishonoring the laws which the gods have stabilized in honor."  The principles of loyalty or obligation to family and observance of religious law justify Antigone's actions.

Creon insists on obedience to civil law.  His edict that praises Eteocles' efforts and denigrates Polynices' shows his insistence on obedience.  Creon argues that deference to his laws is the most important quality in Theban society. Ismene shows how disobedience to Creon's laws carries grave danger.  She is shocked that Antigone would want to challenge what "Creon hath forbidden" and that she herself has no strength to "defy the State." Creon also believes if his laws are violated, the nation or community is left vulnerable.  When Haemon pleads with him to reverse Antigone's punishment, Creon responds that he will not let "the mob dictate my policy."  He underscores this to Antigone herself when he says that "No woman shall be the master while I live."  Creon equates his laws with the supremacy of the state.  As a result, he exhibits how protection of nation or community is extremely important to his tenure as ruler.

In Creon's and Antigone's stubbornness, both display a protection of personal dignity.  This principle propels the dramatic conflict.  Both Creon and Antigone insist on their approach being the only acceptable path.  It is why both of them alienate family members who beg them to reconsider their choices.  To move from their principles would mean a loss of personal dignity.  Antigone will not let her dignity suffer in the face of Creon's law.  She shows commitment to her dignity with her death.  At the same time, Creon will not allow Antigone's example challenge his.  Their own suffering and the suffering of those around them increase as they protect their personal dignity.