In a bolt gun, you really asked for a .243Win. Low recoil, decent accuracy, inexpensive to load for. I use my .260 more than my .243 now, but teh .243 is a great cartridge. Platform, Tikka or Rem 700 would be my choices, but nothing wrong with a Savage, Winchester, even a Ruger. Pick the options you want and go for it.

If you want an AR-15, you could consider the 6x45. Just a different barrel and everything else the same as .223. You will lose some velocity on the .243, but still plenty for Whitetails, prairie rats, coyotes.