who should be in charge of getting the vaccine out

[Del Tachi]

For essential healthcare/frontline workers:  the Fed govt buys it, then distributes to states once they have a distribution plan in place  

For most people:  medical facilities/orgs/whoever buy it, the insurance companies (including Medicare and Medicaid) and/or patients pay for it

For vulnerable populations (the VA, Indian reservations, etc.):  the Fed govt buys and distributes it through existing programs for these groups

lol at everyone saying we should use the military.  Our military has better things to do, and it's not like our country is lacking existing healthcare infrastructure to distribute a vaccine.