Do you have to become a monk, before you become a priest?
A monk is a member of a Religious Order (such as Dominicans, Franciscans, and Jesuits).
Some of these monks become priests (our Holy Father Francis was/is a Jesuit monk). But many priests are not members of any Religious Order, and have never been monks.
These are Diocesan priests. In the United States, most Catholic Parishes are administered by Diocesan priests. The “superiors” of these priests are the Bishops of their Diocese.
Religious Orders operate “outside” of the normal Catholic pastoral hierarchy. The entire earth is subdivided into various Dioceses with Episcopal (Bishop) leadership. Canonically, each Bishop is spiritually entrusted with every layperson within his Diocese (whether Catholic, or Baptized, or pagan). The laity “belong” to their Bishop, and they are his responsibility.
A Religious Order enjoys great autonomy within its own ranks, but may minister to the laity only at the pleasure of the Bishop of that Diocese.