Final answer:
For an 8-year-old with new onset rapid, deep, labored breathing, a chest radiograph, collection of sputum samples, and measurement of blood oxygen levels with a pulse oximeter would be the initial diagnostic tests to consider.
Step-by-step explanation:
If an 8-year-old presents with new onset rapid, deep, labored breathing, the first diagnostic test to consider ordering would likely be a chest radiograph. This imaging test can help visualize the lungs and identify any abnormal patterns, such as fluid accumulation, that might suggest conditions like pneumonia or respiratory distress syndrome. Additionally, given the symptoms, it would be prudent to collect sputum samples for microbiological evaluation, which can help diagnose infections such as influenza or bacterial pneumonia, and to use a pulse oximeter to check for hypoxemia.