Final answer:
The first task a nurse-manager should perform is to appraise the care needs of each client before assigning staff based on the patient classification system.
Step-by-step explanation:
When a nurse-manager is applying a facility's patient classification system (PCS) to determine the unit's staffing needs before the beginning of a shift, the first task they should perform is to appraise the care needs of each client. This step is crucial because it ensures that patients are assigned to nurses based on their individual care requirements, which could vary significantly from one patient to another. Only after understanding the levels of care needed by patients, can the nurse-manager make informed decisions about staff assignments to ensure optimal care and patient safety.