Chinese geese are the smallest breed I know of, maybe ten pounds at the fattest. I know of the Oregon mini's but don't know the size relative to the Chinese.
Chinese are the loudest geese (so I've heard) with the most vocalization, but they are also known to be the best "pet" geese in terms of temperament and getting along with others.
Whatever kind you get, make sure that they are raised with lots of exposure to the other birds, even direct exposure once they are old enough to go outside. And have you daughter handle and cuddle and "play" with the geese as much as she wants so they will imprint on her. The only thing about children and geese is that children might hold a gosling too tightly around the ribs and accidentally suffocate them, but other than that, they need lots of contact from her and you every day for them to stay friendly.
A goose that is "used" to you, ie, sees you every day, but doesn't bond with you, can become aggressive later. The ganders, mostly. They are familiar and therefore not afraid of you. My poor adult daughter discovered this with my gander Petey Peters.