I had the pleasure of having a hand fed baby rosy bourkes parrakeet as a pet about fifteen years ago and they are precious and adorable. Not the smartest birds around, but very sweet and much quieter than a cockatiel. My little "Bourk Bourk" was very devoted to me and the most docile little bird. He always had free-flight and was as tame as could be.
Another uncommon but splendid small pet bird is a handfed lineolated parrakeet. A bit noisier than a bourkes, but a good deal smarter, and the normal color lineolated is still fairly inexpensive, if hard to find. They remind me of a south american version of a budgie.