Havanese would be my suggestion from the toy group of dogs. Very social and friendly. Grooming required.
For a big larger and sturdier but also much higher energy dog, Boston Terrier. Outgoing socially, not as "terrier" as the terrier group. Wash-n-go coat.
But, there is a lot to be said for just going down to the local humane society and meeting some smaller/medium dogs. Unless the 20 lb limit is due to housing restrictions, you might find a good match in the 20-30 lb range so keep an open mind as weight and build can be deceiving (tall and lanky, short and stocky etc). If size matters though, only consider either adult (1+ year old) rescue dogs or purebreds from a well researched, reputable breeder. It can be hard to guess breed and size for shelter puppies and some runts at 8-10 weeks grow up a lot bigger than expected.
With a small child, an adult dog can be a great thing. No trying to rush a puppy out the door to pee at a moments notice while your kid needs attention at the exact same time, no sharp puppy teeth biting at everyone and everything, fully vaccinated so no restrictions on walking in busy areas. A small breed dog aged say, 1 to 3 years, is still very young in terms of having a full lifespan ahead but is fully mature in terms of mental/temperament status.