I'll use 220 gn round nose from Hornady with exposed lead end. Why that heavy? Dangerous pray hunt. Don't want to take any chances. But also don't want to flinch from a larger cartridge.
1-10, out of 308 should work fine with 220 but bits on the edge depending on velocity and overall bullet design. If it was a 300wm you would be okay but the velocity on the 308 will be much lower. As asked above, why a 220 out of a 308? You can always try and "stretch" things but a 1-8 twist would be a sure thing, but again I don't know the bullet you want to shoot. 220gn is a little vague.