For Arizona:
Arizona requires drivers to have car insurance that meets or exceeds the following minimum levels: Bodily Injury Liability Coverage:Minimum $15,000 per person / $30,000 per accident. Property DamageLiability Coverage: Minimum $10,000.
This is the base. You'll want to make sure you have Collision and perhaps Comprehensive as well (Comprehensive would cover things like hitting deer, where Collision covers car collisions.
Another way to look at it is that the "bare minimum" will cover damage you do to the other people and their cars. You will also want to have something that covers damage to you and your car as well. This is important because even though the theory is that if you ever get into an accident, it won't be your fault and the guilty party's insurance will cover the damage, a lot of people drive around without insurance. The less you pay, the higher your deductible will be. I'm comfortable right now with a 500 dollar deductible to insure damage done to my car. I do not have towing because I have AAA or rental provided because that's in my extended warranty. Another thing to consider is whether or not you will have other people drive your car, that's a separate thing to cover (I do not let anyone drive my car). So consider all that, have an idea of what you want as you research online. A lot of insurance companies will provide a free quote, so experiment! After you narrow it down, talk with an actual agent and see if you can haggle. This will also allow you to ask questions and get a comprehensive idea of what you are getting.
Edit: Third gen has made good points as well. I don't get insurance through AAA, just the roadside assistance. No real reason, it's just what I'm use to
Edit 2: Going over my policy, I apparently have some Pet Injury Collision Coverage. In my case, the insurance would pay out up to $500 dollars for vet bills if my pet (cat) got injured. Since you plan on getting a pug, you might want to consider/look into this.