I think the best family dog out there is actually the pit bull terriers. If you get a good shelter dog (there are TONS of them in this breed) or raise one from a puppy (still TONS of them in shelters everywhere). Their main problem is dog aggression, so you'll want to make sure the dog you pick out is friendly towards other dogs.
Other than that, they're awesome. Very smart and fun. They don't have near the health problems that so many other breeds have, and I've seen them as small as 30-35lbs, perfect for a small-ish home you're describing
. I love our labradors, but if I were to get another dog, I think it would be an APBT or a Staffordshire Terrier.
I also think it would be easier to get a pup that's around 6mo-1yr or so, already housebroken, from a shelter. That way you don't have to worry about housebreaking or leash training (if it's a good shelter, they should already be walking a dog that age on a leash daily). Additionally, a good shelter will do plenty of behavior tests for other dog aggression, etc, so you'll know about that all ahead of time.
If a bully is out of the question, well.. I just can't think of a better breed for your situation right now! Maybe a poodle, but only if you can find one over 2yrs, retrievers (which poodles are) can be a bit mouthy and chew up to about 2-2.5yrs. Otherwise, a poodle (without that sissy haircut please) is very sweet, and the medium sized ones aren't all that yappy. The toys can be annoying.
EDIT: Yes, I've had personal experience with all the breeds listed, except I've never owned a poodle, but have had several friends that did and have house-sit for poodle owners before.