Suppose one person is popular but repeatedly misrecites important passages, while another has reliable recitation and understands the essentials of prayer. Popularity alone is not the right criterion for leading the congregation. Similarly, recitation skill does not excuse mistreating others.
خِيَارُكُمْ refers to good qualities and قُرَّاؤُكُمْ to competence in recitation. In both words كُمْ means “your” in the plural.
Fitness and responsibility provide the essential principle: an appointment should consider the skills needed for the duty rather than personal popularity.