Going through the same thing. My kids are 9 and soon to be 16. My daughter wants a parrot for her 16th bday. I will say that I not only did research, but she has done research and we have spent some hands on time with birds we has access to. I wanted her to pick sensibly and not solely on looks.
I will start by saying that she is realistic. She knows she is uncomfortable with anything larger than a grey or anything with an intimidating beak size. We have had the opportunity to handle multiple alexandrines, she is turned off by their beak size and did not care for their personalities. They are a bird that quickly regresses if not handled on a daily basis. I can't comment on the amazons, they were not something that appealed to her, as far as greys, they aren't snuggle bugs as a general rule of thumb, but the timnehs are said to be the gentler of the two. What strongly interested us, based on a comfortable size for us ,disposition (remember all birds are individuals) willingness to interact, activity level and bonding were conures (there are some that have the ability to mimic more than others and may not be as prone to screaming and are larger like the blue crown conure and the Patagonian), the white bellied caiques (love them!!) and the Hahns macaw. We have a house in the country so the loudness was not a determining factor, all the candidates are known for their playfulness. We chose a Hahns Macaw, she does not know it yet and will find out on her birthday, she is content with any of the birds we narrowed it down to. Had there been a White bellied caique available at the time of me placing a deposit, I would have strongly considered it. It depends on how active your family is, age of the children or those that will be handling it, how hands on you will be, all birds need interaction, some are more content playing alone than others, the cage size you will need, proximity to neighbors and their tolerance for noise....if you have a chance to venture to a bird shop, you may want to go in and check out what is available, spend some hands on time if possible. All birds have a cranky side, you have to take the good with the bad, but if mimicking is not high on the list, check out the wb caiques, they are very active, clowns, the more activity in a family the better for this characters, and they can pick up a few words, but their playfulness is a hoot.