The 7-08 is an excellent deer cartridge.
Plenty of power, so no need for expensive premium ammo. Winchester Power Points or Remington Core Lokt will work just fine, and are a lot less expensive.
Premium bullets would be a good choice for elk or moose
And I looked, and behold a pale horse: and his name that sat on him was Death, and Hell followed with him. And power was given unto them over the fourth part of the earth, to kill with sword, and with hunger, and with death, and with the beasts of the earth.