What you need is a breed-specific rescue. They generally have young adult dogs of the breed you choose, and they will be able to tell you a lot about each dog's personaility and match you a good fit to your life, AND most are potty trained as a puppy won't be.
Search "poodle rescue" and your nearest metro area, or whatever other breed you like. Schnauzers are also hypo-allergenic, although more challenging to train.