You have a great budget for renting in Scottsdale. I'd first look in your work zip code so you don't have much of a drive and then you can look further out as well.
Renting with a Pit Bull may very well be a problem. I completely understand how loving they can be and have nothing against them, but I have heard of landlords having a breed list of dogs they will not rent to. It's just something to be aware of and not surprised about.
You will find quite a few retirees in Scottsdale (and many other areas as well), so just be aware. Scottsdale costs more and the people who tend to have the money to live there are well off retirees. However, there are lots of families and "younger" people who live there as well. A pretty decent mix I guess. The nicest thing about Scottsdale is that it's kept really nice and clean ($$).

There are a ton of other great things about it though. I love Scottsdale!