Welcome to the forum...
How much experience do you have shooting 7mm Mags or 300 Mags??? If you can sit down and handle the recoil of 10-12 shots, then have at it, most can't...
Any caliber including .243, .260, 7mm-08, .308, 25-06, 270 or 30-06 in a modern bolt action rifle with a good scope in 3x9x40 will do all you need to do...
Also, while the Triple Shocks are great bullets, I'd stick with standard cup and core or Nosler Partitons and shoot more for less...They will do just as well on the smaller animals you mentioned...