The recipe for the oil to be used in anointing a priest and the articles used in the tent of worship is given in Exodus 30:23-25.
“Take the finest spices: of liquid myrrh 500 shekels, and of sweet-smelling cinnamon half as much, that is, 250, and 250 of aromatic cane, and 500 of cassia, according to the shekel of the sanctuary, and a hin of olive oil. And you shall make of these a sacred anointing oil blended as by the perfumer; it shall be a holy anointing oil.
Some versions translate these ancient measurements into modern equivalents. For example:
Mix a gallon of olive oil with the following costly spices: twelve pounds of myrrh, six pounds of cinnamon, six pounds of cane, and twelve pounds of cassia. Measure these according to the official standards. (Exodus 30:23 CEV)
We are not given specific reasons for the ingredients, but presumably the olive oil was used as a base because it is the most commonly available oil in Israel.