I am snowbirding this Winter in Sun City West. If you are a seasonal resident and would like the easiest-to-get permit to carry that is honored in Arizona...get the Utah permit!
The Utah permit is valid in about 30 States (see http://handgunlaw.us for coverage maps), and only requires a short class (about 4 hours) and no range time! It is one of the most sought after and common permits issued in the United States due to its broad range of coverage.
If interested in setting up a class, either at my residence in SCW or yours, please let me know...it will be fun!
If you are a permanent resident of Arizona, then you need to have the Arizona permit. Normally that requires a class and range exerise. However, if you (even as an AZ resident) obtain the Utah permit, you can forego the Arizona class and range exercise and apply to and receive your Arizona permit based upon holding a Utah permit.