Are you looking for antlers or meat? Deer, elk or pronghorn? Archery, blackpowder or rifle?
BTW, I am unaware of any big game hunts (rifle) on Ft Carson that don't require preference points to draw the tag. And if you do eventually draw a tag, sometimes you are severely limited to the areas on post where you can hunt. As you know, training is the priority - hunting is somewhere far below that on the list.
If you want to see some nice animals on post, talk to the range control officers - they know where they hang out.
Shoot me an email/IM if you want any specfic recommendations.
Rifle and archery. Any game that tastes good. Won't be doing any taxidermy.