Welcome to the forum!
I have a GCC named Callum. I don't have any experience with Quakers, so I will speak on my GCC only.
Callum is definitely only a one-person bird. If my friends or visitors try to handle or pet him, he will first back away, and then bite them if they continue to pester him. He loves my grandma and I, but that's the extent of his social-ness. However, I wasn't aware that the Pak-O-Bird existed and I didn't socialize Callum as much as I would have liked. If I ever do get that backpack, Callum will come with me.
Callum is loud for a GCC. Obviously, there is no such thing as a completely quiet bird, but Callum is loud. If I am out of the room and he can't follow, he will call for me. I've tried training that out of him, but I've given up. If he can follow, he will land on my shoulder and just chill with me. Callum is also a singer and loves to squeal along with songs, or the random tunes I make up and sing for him. If I'm playing video games (like, Overwatch), Callum will screech when I do or just make noises in general. He loves to laugh at me when I get frustrated.
Callum is also fantastic at imitating sounds. Callum beat-boxes, laughs, and says his name, nicknames, kissy noises, and is working on a number of phrases.
Callum wants to be with me constantly. If I'm sitting at my computer (like now), he will jump between my shoulder and chair and constantly groom my hair (I have shaved hair, so he loves to groom that), my cheeks, eyelids, eyebrows, lips, and my ear until I notice him. I can see why people could think that's a negative behavior, but I don't mind so long as he is gentle. If I'm playing games, he has to be right there. I don't mind it and I try to include him in everything I do. I'm home a lot of the time, so he gets plenty of love and free time.
Callum also hates random things. My inhalers? Hates them. He puffs himself up, headbobs, and bites them. If he can't get to them, he will bite me because he's so mad. I'm pretty sure he broke the cartilage in my ear from being angry that he couldn't reach my inhalers while on my shoulder. He hates water bottles and soda pop bottles. He hates my PS4 controller. He hates a lot of things, mostly brightly colored things. We are working on it, but he can and will bite me.
Now, I can't end it there. Callum is a MAJOR lover boy. He loves getting kisses, he loves kissing my lips (and making a kissing noise), he loves laying on my chest, he loves cuddling. He has this weird thing where he'll push his head up to my nose and then have me breathe on him. I think he enjoys the warm air rushing through his feathers. He loves getting kisses from me. This bird craves my attention and my love. Callum loves to watch my screen when I play video games.
All in all, I wouldn't trade Callum for anything. He has his "cons," his quirks, and his lovable attitude, but GCCs tend to be nippy and orientated towards one person. He loves me and I love him to death. Thankfully, I've lucked out on Callum not being too nippy and giving warnings when due.
He does get jealous of me loving on my other animals, but I think that's normal bird behavior.