If I were an average sized guy, with a little shooting experience & wanted to hunt mostly deer, occasional elk, looking for my firstest ever gun.....
Tikka T3x in .308. Totally capable on elk out to 500yds.
Buy a few boxes of reduced recoil ammo then go to the range. No more than 20 shots at a time until I was happy with my accuracy at 100yds.
Then step up to some full power, but light bullet loads, rinse & repeat at 100.
Then step up to some full power 165/180 gn loads & start working your way out to 500yds. Once you hit a distance where 'definitely' becomes 'probably' you'll know your max hunting range.
If you do this with, say, 20 boxes total in the space of a year, I honestly reckon you'd be a more proficient shooter than 90% of the nerks in the woods.