To your specific questions
Internal Medicine may be one route to take. Keep in mind that Internal Medicine is a busy department and that they may be at capacity at one campus (AZ, FL or MN) but not at another. Be sure to inquire. Regardless of which campus you are treated at, you will benefit from cross-campus, cross-specialty expertise. The multi-specialty, integrated, collaborative team approach is practised by all departments at Mayo Clinic, not just Internal Medicine. For example, if your systemic condition is related to the endocrine system, your intake may be through the Endocrinology department and your care would be "quarter-backed" through that department should you need to be seen by other specialty areas.