First, such a requirement would be illegal, since the only approved vaccine (Comirnaty) is NOT generally available in the US.  You cannot require people to get a medical procedure which is still considered experimental, so your consideration is premature until Comirnaty is actually available in Virginia or another product is approved.

Second, the COVID vaccine does not prohibit transmission of the disease.  Those who are vaccinated can still get and transmit COVID, so there is no public benefit to mandating its use.  Any benefit derived from being vaccinated is completely individual, so it should be an individual choice.