There is little evidence to support any link between vaccines and Gulf War Syndrome.
military immunization schedule
While there is a mumps outbreak on a Navy ship, it is important to keep in mind that in the pre-vaccine era, many more sailors would have gotten sick and they would have more complications.
You will need some extra vaccines when you enlist in the military.
Smallpox has been eradicated, but a smallpox vaccine is still available – just in case.