If the money is intended to be a stipend for the priest for celebrating a wedding, baptism, or funeral, it is given directly to the priest. If the money is intended to pay for the use of the church, then it is made out to the parish. Ordinarily, a family arranging for a wedding, baptism, or funeral would make out two checks: One to the priest for his services and one to the parish for the use of the church. Additional stipends for servers and liturgical ministers are given directly to them unless the parish includes those stipends in the use of the facilities and distributes that portion of the money for the family. Ask the parish office what is the customary practice in your area.
As for how to make out a check to a priest, you can put either “Fr. [Full Name]” or “The Rev. [Full Name].”