I live in Florida, but worked as a traveler in Arizona from Oct through Dec of 08. Do I need to file an Arizona state tax return on top of my federal return, and if so, which one? Non resident or Part year resident?

Yes, if you were in Arizona, then any income earned during that period is to be reported to Arizona. Read: Your U.S. Tax Return: Working or Living in Two or More states

You file as a non-resident for Arizona.