As recoil is one of your main considerations, here’s some data I pulled a while back comparing rifle cartridges. There are multiple opinions on energy requirements for bullet expansion and penetration - I used 1,300 ft lbs for this. For most hunting scenarios of shots under 400 yards all of these will get it done - find the rifle that fits you the best and is in the budget - that’s an entirely different argument with plenty of opinions
7x57. 12 lbs of recoil with 139 grain bullet. 1774 ft lbs at 200 yards.
Max effective range 400 yards - 1314 ft/lbs energy.
7mm-08. 13lbs recoil with 139 grain bullet. 2042 ft lbs at 200 yards.
Max effective range 500 yards with 1311 Ft/lbs energy
6.5CM. 13 lbs recoil with 140 grain bullet. 1773 ft lbs at 200 yards. Max effective range 400 yards - 1379 ft/lbs energy
308 Win. 16 lbs recoil with 150 grain bullet. 2176 ft/lbs at 200.
Max effective range >400 (1543 ft/lbs at 400 drops to 1287 at 500).
.270 win. 17 lbs recoil with 140 grain bullet. 2042 Ft/lbs energy at 200 yards.
Max effective range 500 yards - 1310 ft/lbs energy
280 Rem. 17 lbs recoil with 139 grain bullet. 2250 ft lbs at 200 yards. Max effective range >500 - (1459 ft/lbs @500)