Press the easy button. Everything from 6.5CM on up will kill those game animals at ranges farther than most hunters can ethically shoot. If you have the skills to take advantage of one of the fast 28 or 30 caliber cartridges, you don't need to ask for advice. But most of us can't make 700-1000 yard shots.
I have owned several 7mm and 30 caliber magnums over the years and sold them all. Right now, 30-06 is my big gun and I haven't hunted with it on over 10 years. My 308 does the same thing out to 500 yards and I won't take a shot anywhere near that far. It recoils less and is cheaper to shoot, which means more practice.
The 7-08 is another excellent choice, but it doesn't do anything my 308 won't do and 7-08 ammo is a lot harder to find. The new 6.5CM is the smallest cartridge I'd use for those game animals. Either of those 3 would be my choice and 308 wins simply due to ammo availability.
But if you're inclined to go with a long action there is nothing wrong with 30-06, 270, or 280. To say one is better than the other is splitting hairs. I'd advise staying away from the magnums. I know the 28 and 30 Nosler don't have "Magnum" stamped on them, but they are magnums.