If you are looking for a dog that is best for an allergic person, there are a lot of choices. The Maltese, Bichon, and Basenji are all dogs that do not shed much. If they are kept clean, they have fewer allergens shed into the environment.
The Basenji also does not bark.
Low maintenance is different. Are you talking about a lazy dog, that does not need to be taken care of all of the time, or a dog that you can put outside and let him wander around the farm taking care of himself? Low maintenance varies for everyone.
Not everyone can meet a dog's needs. If you have too many things you do not want, a dog is not a good choice. In the past, at least some people were around the house more (a wife, kids) and the dog was not isolated.