300 Winchester magnum will do all that you ask, and more. I shot one religiously for over 30 years, and never had anything walk away. Stay away from the lighter bullets, they tear deer up. Minimum 180 grains with 200 being better. You can load it down for deer, if you desire, and full house loads for moose and elk. Extremely accurate and excellent trajectory. Recoil is not bad off a 300. A 338 is not pleasant to put a box through at the bench. I would shoot my 375 H&H all day, but that 338 was just plain nasty. For an all around you can't beat the 375 H&H. Doesn't wreck the smaller critters, and is real comforting if you meet a grizz at 20 feet.