My primary considerations would be:
First - availability of ammunition or reloading components
Second - reliability
Third - "applicability versus" (meaning what would I expect to actually shoot with it)
Forth - "facility (or "packability) I don't want it too big or too heavy. It must be short in length, weigh in a light as reasonable, easy to pack along with me, etc.
My first thought would be "The Gun That REALLY Won the West" a double barrel shotgun. But the truth is that, effectiveness aside, I believe the ammo is less efficient/precise/ and more "spendy" from a materials-required standpoint.
And all through the 50s, 60, 70s 80, 90s, etc I always read and believed that if I could only have one gun, it'd be a 22 rimfire rifle. And with one possible exception, I still believe that today.
That exception is that the previous 50 years have taught me that, here in the 21st Century, out in the wild places, either times have changed or I have. I've come to believe that the real danger in the bush is two-legged. And worse, those same critters, however rarely seen in the wild, swarm worse than rats in the major metropolitan areas.
Defense rises to the top of my concerns.
My "one - gun" choice today, would be a Marlin or Rossi Trapper length lever rifle, preferably in 44 magnum, then 357 magnum, or third, A M94 Winchester Trapper chambered for 30-30.
And from real experience I know I can keep myself supplied and well fed with small game using either 44 or 357 light loads (or 44 or 38 Special rounds) in my Trappers.