While we at Help Shelter Pets are dog owners (one of us also loves cats but the other is allergic to them), for me it was easy when I picked the Pomeranian as my breed of choice. But it might not be so easy for others to choose a compatible breed of dog or cat.
I just read about NYC's Jacob Javits Center holding the annual "Meet the Breed" event hosted by American Kennel Club. The variety of dogs and cats on display is enough to send you to the shelter for a mongrel (which is a good thing!), but it will also give you enough information to make an informed decision about the animal that best fits your lifestyle.