[@Ghost Queen] Military-grade body armor (in the latest fashion, of course!), a rifle/guns, an earpiece to communicate with HQ, etc.- pretty much standard military equipment, honestly. How much weaponry a soldier packs also depends largely on their Gift. If they have a particularly strong power, they would probably be less decked out than someone who can only freeze water lay  or something similar. Some soldiers also like using swords and whatnot, although that's largely for aesthetic more than anything. Erubesco adores its theatrics.  

EDIT: When not on solo missions, Erubesco military forces also have armored vehicles for use in transporting goods and doing general surveys of the land, among other things. They also have teleporting Gifted among their members, who serve as a mode of transportation when a vehicle isn't necessary.