I would get a 300 weatherby or 300 win mag. You definitely need to get a muzzle break. I would not go any larger in case capacity due to recoil in the light factory rifles. I like your choice of 30 cal because you can shoot 100 grain to 240 grain bullets.
If you were going to build a custom rifle
I would build a 16lb 300 Norma mag. The 300 Norma mag is basicly a shortened 338 laup mag case necked down to 30 cal. It is a lot more efficient than the 300 ultra mag meaning you can shoot the same bullet at a higher velocity with less powder.