At the age of 16 (1969) I had to make some of the same decisions.
I had the advantage of being an Oregon native with a family hunting heritage behind me.
I chose the .270 Win as my primary firearm and have never regretted it.
Factory ammo is not expensive. Recoil is negligible and trajectory flat.
It works very well on both deer and elk.
I suggest either a .270 or a 30-06 as a starter rifle for any new hunter. They will do it all and last a life time.
Good luck and good hunting.