The muzzlebreak on my 7mm WSM that I had installed by Williams Gunsmithing services (the Guide Series model) has been a godsend. Some of the best money that I have spent. The feedback that I have gotten at my local range (Rio Salado in Mesa) hasn't been too bad either, but I have had to double-up with ear plugs and muffs so my ears stop ringing.
That being said, if I were you, I would purchase either a 30-06, a 270, or a 25-06. All of these should handle the game in Arizona, maybe with the exception of elk and black bear for the 25-06. The advantage of the
25-06 though, is that with a proper load of 115 to 120 grain bullet (i.e. Sierras 117 gr. BTSP, 120 gr HPBT, or Noslers offerings) is that it provides the same level of performance as the 270 with a reduced amount of recoil.
I think you are being wise, though, in by-passing the magnums for now and concentrating on a good, proven caliber. You cannot go wrong with any of the three I mentioned, especially the 30-06. I've had three since I started buying when I was 19 (I'm 39 now), and each has been better than the last. It, a .22, and a 12 ga. shotgun are the staples of my collection.