Keep in mind that the recoil without a muzzle brake must be something you can handle for at least 30 shots at a range. Most people can't handle repeated recoil from the 30 cal magnums or above for more than 10 to 15 rounds at a time, which means you'd need to have the rifle fitted with a muzzle brake, and wear plugs while hunting. Muzzle brakes are LOUD. Also, some of the rounds suggested here are hard to find at the local gun shop unless you order them. They also tend to be quite expensive. A 270 winchester, a 280 Remington or AI, a 7mm Mag, a 308 (with the right loads), a 30-06, or any of the short magnums in 30 caliber, or a 300 winchester Magnum will do what you want. The magnums will do it marginally better, but the -06 is probably the most effecient in terms of recoil, bullet weight, accuracy and killing power. Next in line would be the 280 Remington or the AI version of the same cartridge. However, the 30-06 can be found in just about every country in the world, where some of the others aren't nearly as available. I'd go (have gone with)with the 30-06.