What Would You Pick For The Following?

All would be fine, but the 7mm and 300 win will have more recoil and are a bit overkill for the game and yardage you listed. Consider the 25-06, 260 remington and 7mm-08 especially if you reload. IF not then I would go with a 308. You can buy cheap bulk ammo for coyote hunting. And normal ammo is as cheap or cheaper than any of the above calibers.