Under section 8 you can select from private apartments, if the landlord agrees to the section 8 requirements or go to section 8 prequalifified apartments.
There will be less pre qualified apartments available, especially in Scottsdale.
Your Section 8 contact can give you a list of landlords that have registered with them. They may not be any less expensive than private apartments however.
Applicants may apply for a Section 8 housing voucher at any county or city housing authority office in their state, and use it anywhere statewide once they receive it. However, priority for vouchers is often reserved for those who reside in the service area of that housing authority.
"In many localities, the PHA waiting lists for Section 8 vouchers may be thousands of families long, waits of three to six years to access vouchers is common, and many lists are closed to new applicants. When wait lists are briefly opened (often for just five days), which may occur as little as once every seven years, there can be as many as 100,000 applicants for 10,000 spots on the waitlist, with spots being awarded on the basis of weighted or non-weighted lotteries, with priority sometimes given to local residents, the disabled, veterans, and the elderly. There is no guarantee that anyone will ever receive a spot on the waiting list."...note per Wikepedia.
Your Realtor can show you a list of apartments to consider.
Jerry Seeger West USA Realty Revelation