The most important thing to consider when selecting a medical power of attorney is whether or not you trust the person. They should be competent and have your best interest in mind.
Many people will select a family member or close friend to be their medical power of attorney. Children are often chosen as POAs by their parents.
Note: Most states have restrictions that ban your primary physician, nurse practitioner, residential health care providers and their employees from being appointed as your medical POA because of their potential conflicts of interest.