I highly recommend Chandler Air Service too. Did my PPL and instrument with them. Just started my commercial with them as well. Great instructors, well kept airplanes and a love of flying there.

ATP is a great school out in Gateway Airport (KIWA)
I got my private through them and wouldn't hurt to looking into but keep in mind that its a FAST paced program and isn't for a lot people.

There is also Sawyer Aviation out in scottsdale (KSDL)
Instructors are great and go out of their way to help you out and understand.
I got my instrument through them also have a great maintenance program as well.

Fleet consists of a
Diamond Twinstar DA42 (Turbo Diesel G1000)
182 (G1000)
172 (G1000)
172 (Standard fuel injected)
A newly acquired skycatcher

But I also would recommend you try looking at
"Westwind School of Aeronautics" in KDVT
I got my commercial single and multi engine through them.
The instructors are great, maintenance personnel are also helpful and cool to talk to and they can help point out how the systems work
Fleet is also great, they have g1000 172's, standard 6 pack 172, carb and fuel injected 172's, twins are PA-44 they have (4) of them.
I commuted from mesa to deer valley just to go there and took me 30 min tops.

I flew to all the local airports in PHX and the airspace is great to fly around, as far as chandler I also flew there and they have great gas prices for aircraft one of the lowest in the area all the time. Chandler airport also have a good tasty restaurant to eat at, and there is a pilot shop right across from them.

Hope this helps you out and this is just my .2 cents good luck!

I did my ATP rating at ATP IWA when I was at Luke AFB. Those guys are squared away and got me through fast. I would recommend it.