which type of parrot should i get for my child?

none if your child is under 13. birds can be fragile and hard to take care of. if your child is 13+ then you could start off with budgies. just do the proper research

Parrots are really a pet for an adult or a very responsible young adult. Not knowing what to do or how to train or handle a parrot can result in a ill tempered animal or one with psychological issues. Not to mention they will live for 20,30,40 50 or 60 years or more. How about a nice plush parrot toy.

How old is the child?  It makes a difference.  Who will be the main caregivers? 

A Parrot is a big responsibility and they can live 40 to 75 years on average depending on the species. Children usually get Parakeets. Make sure the kid doesn't try to handle the bird constantly as it is stressful to the bird and I've seen birds die form this.

Short answer: something small and docile, like a cockatiel. Save the expensive ones until the child is old enough to make a decision and live with it for the rest of his/her life.

Long answer: Head to your library and ask the reference librarian to get you a copy of an article on interlibrary loan. It's in the 1988 volume of Bird Talk and called "Pick a Perfect Parrot". Note the indefinite article; what is perfect for one person might not be perfect for another. The article discusses the pros and cons of different kinds of parrots.

https://www.youtube.com/watch?v=5uYNTOpOhBo

Red parrot