I think that the route you should take depends on your circumstances. If you are able to get get into a BSN program right now, can afford it, etc. then it would make since on a timeline to go that route rather than get your ADN and then go back for your BSN, especially with a 3 semester wait. If you can't then I don't see a problem with going the ADN-BSN-MSN-?
I don't know anything about schools in AZ, but generally I think if it is an accredited state university then the program will be recognized.