Well as you know each bird will be different, but there are species (parrots come in species not breeds, though some would argue that hybrids such as sunday conures or camelot macaws are breeds) that are known for being quieter.
Are you looking for more of a snuggle buddy? clown? talking ability? What are your other priorities?
My Eclectus talks, but only screams when he is sick (Seriously, one scream and he goes straight to the vet!) and many Eckies that I have met have been similar. However, a screaming Eckie is a force to be reckoned with. He is a great talker and his voice is sweet. When he chatters he chatters in English which is cute. One consideration is that Eckies need a mostly fresh food diet and do not do well with seed based OR pellet based diets. And the poop reflects that!
My Pionus is very very quiet, but came to me a screamer and still has periods where she reverts. When she screams it could peel the paint off the walls, its like the loudest fingernails on a chalkboard that you have ever heard. But Pionus are generally considered good apartment birds especially if you are looking for a smaller bird that really has a "parrot" look. My female does talk, she says a couple of phrases but her voice is raspy and difficult to understand. Maxamilians Pionus are supposedly the best talkers in the Pionus family.
Green Cheeked Conures and others in the same family like crimson bellied conures and maroon bellied conures, and considered to be the quietest of the conures, and I find them to be more addictive than potato chips. I think I can safely say that green cheeks are my favorite species of parrot. They need a lot of cuddles, endless toys to destroy, and firm boundaries. None of mine talk but I have had some fosters that did, it was difficult to understand. Conures have a rep for being "nippy." I hate that because I think people use it as an excuse for their bird to misbehave. I have had several gccs come tome as biters but with some effort that can be worked out. None of mine are biters anymore, and no one would call any of them "nippy."
Cockatiels are so sweet! Adorable personalities, great whistlers and often god talkers, smart, come in tons of colors, tend to accept new flock members easily, rarely bite out of hormones or territorial issues or anything like that, really only when they are very very frightened or a human has taught them to bite. I consider cockatiels to be pretty much the perfect pet
Indian Ringnecks, my loudest bird is a ringneck, but so is my quietest. These guys seem to have such a wide range!Males are often good talkers, they are all super smart. They tend not to do as well as other birds when their wings are clipped. They also tend not to be as snugly as many species but they are curious and smart and social and STUNNING and come in lots of colors.
Budgies and Love Birds I do NOT suggest for apartment living if noise is a real concern.
But that said, I and my whole flock live in 600 sq ft in Hawaii, and all the windows have to be open constantly and our neighbors are literally on top of us as we live in a condo. None of my neighbors have ever mentioned any noise. A lot of the noise factor is really a training and environment issue. Yes, some species are louder than others, but a bored lonely cockatiel may drive your neighbors up the wall but a well entertained and content Macaw may never bother them at all.
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