The above classes of qualified applicants shall be
considered as separate and successive lists of eligibles. The governing
body shall first appoint all qualified applicants in Class I and then
those in each succeeding class in the order above listed and shall
appoint a person or persons in any such class only to a vacancy or
vacancies remaining after all qualified applicants in the preceding
class or classes have been appointed or have declined an offer of
appointment. Within each such classification, duly qualified applicants
who are veterans shall be accorded all such veterans' preferences
as are provided by law.