Dunno what being in the infantry has to do with it, but my dad raced rally, and I learned to drive in one of his Cooper S models. I could have impressed the hell out of the MTO instructors with a handbrake turn to scrub off speed on a gravel road but chose not to.
It's not expensive, you can get in in one of the lower classes with pretty much any POS (RWD is way less expensive - think old 280Z or the like, all it needs is a cage, 5-point harnesses and kill switch) but you need a co-driver, a wrench monkey, a trailer not so much to get it to the race but to drag it back if you crash and some sponsors, even if you're just going to be doing Tall Pines and local events.
One tip, and I'm just gonna bold this for emphasis: do not enter your daily drive in the rallycross events sponsored by your neighbourhood rally club, no matter how many times they tell you nothing bad is going to happen. In the rally world, having your car become 18 inches shorter is no big deal. To you, it might be.