For running just around the post, the individual soldiers are very likely just to use their "POVs" (personally owned vehicles) if they're on a CONUS post (can't speak for overseas, though). Whenever I had to run paperwork to battallion, which was about three miles away, or coordinate training sites with other units, I always used my car to get there. If it was something more official, like driving the commander around or doing staff duty, then it was a military vehicle. And especially if it was going to any of the training sites, every vehicle had to be military. The company commander would likely be in a HMMV, and they'd use the HMMV.
I know there are all different types of HMMVs, but in all liklihood, you probably don't need to be more specific than to call it a "Humvee." The reader won't have any trouble figuring that out. I was in a transportation unit, and we usually called the vehicles by their numbers, like my platoon's deuce and half--It was always "Oh-Two." The vehicle for the commander was always "The commander's vehicle."
