you could look into Samoyeds. They're known as one of the supreme kid dogs. They're a medium sized dog.. sweet temperment, smart, and generally very clean dogs.
detractors - they aren't obedient dogs, they're very sweet natured, and very quick to learn, but they're not the type of dog with an "oh please, please tell me what to do" attitude. They will work for a paycheck - treats or playing. I like that, because I can respect that attitude (I also work for the paycheck :-). ) They require quite a bit of grooming, and they are *not* outdoor dogs. AZ is really too hot to leave any dog outdoors during most of the year, and your sammy is going to want to hang out in the same general vicinity as you.
the advantage of a purebred, is that if they're bought from a good breeder, you are more likely to get a consistent temperment - it's true that some purebreds are 'tempramental' but that depends on the breed, some breeds *should* have a certain type of temperment - Akitas for example, are supposed to be the type of dog devoted to their family, and be wary of outsiders - that's not a bad temperment, it's just what the dog is supposed to be, so that's why you're doing your research into different breeds. Also, some breeders don't focus on temperment, and you can get bad temperment there too. Mutts are just as likely to have bad temperments, but they're also the ones the shelter puts down as unadoptable.
a good breeder will also do health checks for their dogs. Dogs need to have their hips and eyes checked, and depending on the breed, also heart, patellas, elbows, and certain breed-specific genetic illnesses.
there is a myth that mutts are more healthy than purebreds. this isn't true for a couple reasons. problems like hip dysplasia are poly-genetic, so if you breed two or more different breeds, it is more likely in the first generation to result in puppies that carry the genetics to possibly have hip dysplasia, but maybe not double up on them enough to have it actually express phenotypically (i.e. the dog will have hip dysplasia.) the other part of this, is very very few mutt owners health test their dogs. I have a female samoyed I may consider breeding at some time. I have spent about $400 to have her hips, elbows, heart and eyes checked. That's important to me to know she's genetically healthy before I consider breeding her, because I'd feel awful selling a puppy to someone that needed a $2000 hip surgery in a couple years.. or bred a puppy that would be in pain it's entire life because of bad elbows, or went blind because of bad eyes. But if you don't test (the case for most mutts) then you wouldn't ever know if your dog is truly healthy or not. Also, a good breeder will want to talk with you and evaluate whether this breed is a good fit for your home - and that's to your advantage to be able to talk with someone that's lived with this breed for years, and knows how they 'fit' into someone's lifestyle - my girl's breeder even offers to let people's she's talked to 'borrow' one of her samoyeds for a few days to see if they like living with the breed.
The Animal shelters are also filled with incredibly awesome dogs; if you go that route, I'd really recommend one that's a couple years old - still young, but old enough so they know what kind of personality that dog has. Also, by then the dog will hopefully have had basic obedience and be housebroken.
I know this a lot of information, and may seem overwhelming if you're looking for 'just a pet' but a dog will be part of your life for more than a decade, so it's important to make a good choice, for your happiness and the dog's.
if you tell us more about what you mean by a 'perfect' dog for your boys, that would help too. my definition of a perfect dog is completely different from a lab persons, or a terrior persons, or hound person, etc.