[wdfifteen]

I would say miniature Poodle or miniature Schnauzer or a Schnoodle.
I don't know if you will find a short haired dog that doesn't shed. Poodles and Schauzers don't shed, but their hair never stops growing so you have to have them clipped every 3 months or so. "Dogs all tend to shed around the same" is simply not true.
I like the pound puppy idea if you have lots of flexibility and time to deal with it if the dog has problems.
It's a more expensive route, but I buy a dog that suits my lifestyle and then give lots of money to rescue organizations around here. It soothes my guilt at not having time an patience to keep another rescue dog. I've had 4.