There are a lot of good suggestions on here. I would only follow it up with driving around the area at different times of the day and different days of the week to get a feel for what it feels like, and whether you'd feel comfortable walking down the street alone. Whatever you do, I'd suggest you follow your gut reaction.
Hello Sabangirl, You have probably received the answers regarding safety and where to get specific answers - once you have decided on an area, buying a home would be a great move. Phoenix is one of the most affordable areas in the country. A monthly payment for home is less than rent.
If you have safety concerns, your best source of accurate and up to the minute information are the local authorities, why not call/visit and ask all your questions, hear all there is to hear firsthand.