308 will work fine, as posted above I would use the heavier bullets.
I personally shoot a .338 win mag, 250 grain nosler partition bullets, recoil is only an issue if you crawl up on it shooting from a bench. Before the .338 I hunted elk with a 30-06 w/180 grain bullets.
NRA Lifetime Member Since 1999
"I ask, sir, what is the militia? It is the whole people except for a few public officials." George Mason