Final answer:
The nurse should first visit the client who has an elevated white blood cell count indicating a possible infection.
Step-by-step explanation:
The home health nurse should first visit the client who has an elevated white blood cell count indicating a possible infection. An elevated white blood cell count, known as neutrophilia, suggests the presence of an infection. White blood cells are responsible for fighting off infections, so it is important to prioritize this client's visit to address the possible infection.