I think that all depends 100% on your daughter. Clearly you will need to be the bird's care taker and willing to tend to the vet costs etc. Being on the forum I am sure you will be an awesome bird parent.
Most people who come looking for advice are already in the right mind for a pet.
If your child is happy to not physically interact with the birds and is calm and can watch or read to the birds peacefully, I think any of the finches would be fantastic. I think if your child is caring and calm and would like to handle the bird someday a budgie could fit. All birds can be frightful if they are surprised, or in a very active household. Children who are high energy can sometimes act unpredictably and the birds can be very fearful of children because of this. Even if you get a budgie there is no guarantee the bird would want to interact with your child.
It all depends on your family and your dynamic. I know I was a very animal oriented child. I got my first cockatiel when I was young and we had an awesome relationship. I also had bunnies and guinea pigs. If your daughter is an animal oriented and sensitive person I am sure any arrangement can work.
Getting any bird is a life changing experience. We need to change our lifestyle for them. --cooking pots, fans, cleaning habits, feeding, etc. We also must have ZERO expectations. Some birds will never really like humans, even some parrots can take years to develop a bond. You will have some idea of how a species will behave, but at the end of the day each bird is individual. If your child can handle that and understand that, you two are going to be a great bird flock!
