V.P.
Hi, T. -
I don't really have any academically educated advice, but wanted to share a few things we've learned. I agree that people become biased when they have a certain breed of dog and they're really good dogs. We did that. My husband and I had a mini schnauzer for 14 years and when he died, we replaced him with a new mini schnauzer puppy - which has not turned out nearly as well as we would have liked. Every dog is different, and the stereotypes of a particular breed don't necessarily carry from dog to dog. They all have their own personality (kinda like kids).
I'd also say that I have several friends and family members who have 4 dogs between them that were all rescued between the ages of 2 and 6. I really wish that we had taken that route, as training a puppy when you have little ones around is quite difficult.
When we had our first dog, we trained it (ourselves, not with a professional). But when we got our puppy, we had a 3 & 6 year old. We've been told since then that puppies will train to the lowest level in the house. In other words, because my 3 year old undermined (unintentionally, of course) all of the rules and simply "played" with the dog all of the time, it was much more difficult to get her paper trained, not jumping, not barking ALL the time, etc.
Just a few things to keep in mind. Good luck!