The agencies/groups that I cited have the strongest experience in both categories. Someone that has performed service for our country would have both experience in investigation and protective detail. FBI, Military Special Forces, etc. would know how to best utilize fire arms, secure perimeters, assess threats, etc. In most instances, they would also have some form of law enforcement background as well. I would see TBI agents or some higher level police positions being good fits as well but Corporate Security is not good enough.
Out of curiosity, who are the candidates you are alright with in the Secret Service?