Best Shoulder Parrot?

Most bird "experts" advise against putting a bird on your shoulder at all (they can and WILL bond to your face instead of your hand, they can be rather difficult to extricate, etc.). I'd suggest not buying a bird at all if all you plan to do with it is let it ride around on your shoulder. Without enough mental stimulation, they will get bored, and will probably try to bite your hair/ears/face, and you definitely don't want that. >_>