Horayot, Chapter Three, Mishnah Six
This mishnah teaches which sacrifice takes precedence over other sacrifices, in a case where both are ready to be sacrificed.
The importance of this mishnah is that it does not just give specific rules for precedence in sacrificial law, but teaches general principles, which are still applied today, especially in laws of prayer.
I) Whatever is more frequent than another takes precedence over that other;
II) And whatever is more sacred than another takes precedence over that other.
III) If the bull of the anointed priest and the bull of the congregation are standing [to be sacrificed], the bull of the anointed priest precedes that of the congregation in all its details.
Section one: Something that is frequently done is performed before something else that is not frequently done. This is learned from the fact that in the morning the tamid burnt offering is sacrificed before any of the special festival sacrifices are offered. Since the tamid is a daily offering and is therefore frequent, it takes precedence over less frequently offered sacrifices.
We should note that this principle seems somewhat counterintuitive. A person would naturally be more inclined to do first that which is special, more unusual, and only afterwards do what is regular and routine. Judaism teaches that it is the routine which takes precedence and not the special occasion. Through this mishnah, we learn to appreciate not just what is ordinary, but to take note of the importance of those things that we do regularly. We should not allow their frequency to diminish their significance.
A couple of examples where this principle is still evoked. During Shabbat and festival kiddush, one first recites the blessing over the wine and only then the blessing over Shabbat. This is because the blessing over the wine is more frequent than the blessing over the Shabbat. Another example: in morning prayers we recite a psalm for each day of the week. On Rosh Hodesh (the first day of the new month) we also recite a special psalm. The psalm that is recited for the day of the week is done first, because it is more frequently recited than the one for Rosh Hodesh.
Section two: In cases where one cannot apply the previous rule, then the rule is that whatever is more sacred comes first. We will see an application of this principle in the next section, and in the next mishnah.
Section three: If the bull that is offered by the high priest for an errant ruling, and the bull that is offered by the community for their having followed the errant ruling of the court are both waiting to be sacrificed, the bull of the high priest takes precedence. This is because the high priest is more sanctified than the general populace, and also because he brings atonement for others (see Leviticus 4:16), whereas they are just being atoned for. This is also hinted at in Leviticus 16:17, And he (the high priest) will make expiation for himself and his household, and for the whole congregation of Israel. He takes precedence over all of Israel.