Like you, I live with "pound hounds." I will never have anything other than a rescue dog. For me, I have learned that in finding the right dog, it is 100% about matching the personality and needs, and has almost nothing to do with breeds. Yes, some breeds will have given traits -- eg - If you live in an apartment with no yard, and work all day, the last thing you need is a dog which needs to run, such as a hunting dog, like a lab, poodle, terrier, and you sure as heck don't need a herding dog. Within every breed, there are numerous personalities, and you cannot say that a dog will work for you just because of the breed. Does the dog have dominant traits, or is it laid back, like the runt of the litter? The spectrum is greatly varied.
That said, I have heard good things about the LabraDoodle.