Horayot 13 - Order of Precedence
When a High Priest needs to observe mourning, he tears his garment from the bottom, and not from the top, like regular priests and laypeople do. He brings sacrifices even on the first day of mourning, just does not eat them, while regular priests do not bring sacrifices.
When one has any two mitzvot that he can perform, he should first do the one that is more frequent, and this is derived from the order of sacrifices in the Temple. If one mitzvah is more sacred than the other, it has to be done first. If the High Priest's bull and the assembly's bull, brought for a court's error, are both standing to be sacrificed, the High Priest's bull goes first - not based on the above rules, but because it is called "first" by the Torah.
If a man and a woman both need food or clothing, the woman takes precedence, because the man can go begging door to door. When both are held captive, the woman is ransomed first.
Art: Jean-Léon Gérôme - Old Clothing Merchant in Cairo