Of course this is an opinionated question. Every teacher on here may differ in reference to this text as the word important suggests a value judgment.
PROCTOR/ELIZABETH: This marriage seems to hang in the balance throughout the scrutiny of the trial and the moral conflict through which Proctor fights. As Elizabeth realizes her ineffectiveness as a wife, Proctor dwells on his previous sin, both wanting to find a new wholeness. This symbolizes the plight of Purtians because to find an absolution for sin was near impossible.
ABIGAIL/PROCTOR: Abby just couldn't keep her name white in the town. Although Proctor knew it was wrong, this relationship is what much of the play hinges on. Had Proctor not denied Abby, his name and his wife's might never have come up because she would have protected him. But because she is not getting her way with him, he will fall.
PUTNAMS VS. NURSES & PROCTORS: This antagonistic relationship occured between groups. Whether the root cause of the fighting was for land or the access to the minister or for both reasons, these folks couldn't find room for agreement. I think this caused many to die because blame had to fall somewhere. This relationship also demonstrated where power reigned in Salem and what corrupt acts one had to commit in order to possess it.