I learned to shoot usin a lever action Marlin .22 .. as a previous poster said, rounds down range and knowledge of how to shoot will get you where you want to go.
Moved up to a semi auto Remington .22 rifle .. I would go out with 3k rounds or so and just plink at a range ..practicin shootin the center out of a paper target.
Moved the target out when it got too easy.
Took my first deer with open sight Springfield 30-06 .. tween the eyes at 30 yards or so.
I was 15 then, had spent a summer shootin crows for a farmer with my .22.
He paid me a nickel apeice and I financed alla U-control and R/C planes I useda fly doin just that

As in Aces High .. it was the finisher after a proper setup:
.. a few hours of trackin thru the snow up at the South fork of the Dearborn River, near Lincoln, Montana.
He heard us and was behind a rock shelf, head popped up framed by bush right at ground level, I whispered to Dad, he had no visual till I fired and the head dropped.
Dad lectured me on bein sure of my shot all the way over to the shelf .. deer was layin at the bottom, 4-point, dressed out to about 180lbs when we finished.
We (my brother, Dad, a friend of Dad's, and I) packed out two miles back to the camp and truck (a '49 international.. went anywhere)
Tip for hunting in the mountains of Montana . . get a good side arm .. 357/44 Ruger or some such.
Be proficient with it.
You have a bear/Elk/Hog pissed off and come out of the bushes at you just frik-kin shoot it till it stops movin.
Rifle can be a hindrance in close up encounters.
They do happen.
Basic training in the USAF ..first day with the M-16 was 'interesting' ..I shot expert ..it was soo much like shootin my lil .22

I useda shoot the center out of my target and then work on the guys next to me -evil grin-
Years later they converted by usin .22 adapters in the M-16 .. made it even more like my lil .22

-Frank aka GE