The bird that I would most like to own is a Blue Macaw. I read this totally awesome book about a girl and her blue macaw, and it is called "Emergence" By David Parker.
She is a teenager girl who emerges from the family bomb shelter after a nuclear bomb has hit, and she now has to try and find any other survivors. The story is her journey across America with "Terry Dactyl", the macaw, and it is one of those stories that once you have read it, you never ever forget it.
So, if I could have a bird, and money was no object, having my own Terry Dactyl to ride on my shoulder would definitely be my first choice.
If you like birds, I definitely suggest reading "Emergence" if you can find it. You may end up wanting a blue macaw, too....