I was in the same boat 4 months earlier. I do work in the IT field however.
Anyhow, from what I experienced almost all employers would want the suitable candidate to start just as soon as the screening process is complete.
In plain English, if they consider you a good candidate and want to interview you, they would want you to be available asap, you being out of State will definitely shy away companies who are in need of someone pronto. Heck most employers would probably notice your address and may not even call you back.
I am not sure about the field you are in but I suggest roughly about 3-4 week prior to your actualy move date would be a good time to apply for jobs but have your resume updated and available on at least a few different job sites for those who might consider you and also wouldn't mind waiting but I doubt any employer who really needs to fill the position would like to wait more than 2 or 3 weeks tops. When you are ready to apply for jobs, I would recommend using a local friend's/relatives AZ address. As far as the phone goes, local number would be nice but not nearly as important since most of the trnasplant do not change their cell numbers right away for whatever reason so just make something up if they bother to ask. But I would not pull this trick unless you are within a week or two of moving down here or be able to fly out if they wanted an in-person interview!
Good Luck!