I have an Umbrella Cockatoo. I've had her since she was 7 weeks old.
She is an absolute pleasure and I cannot fault her in any way. She is the easiest animal I've ever had. and I've had horses, ponies, dogs, cats, snakes, tortoises...and managed a game reserve!
We brought Bean home at 7wks. She was still feathering and was full of attitude. Fluffing up everytime we went near her for the first few days. After the first 3-4 days she realised we weren't going to hurt her, and over the next few weeks she became more sure on her feet, and feathered out etc. She would fall asleep in the crook of my arm every evening. Such a sweet baby. She doesnt even know HOW to bite, she has never bitten anyone, even now as an adult.
I was very careful when she was small not to spend too much time with her. she got an hour a few times a day. The biggest mistake people with Too's make is spoiling them, because they are so cuddly. Then when the novelty wears off, the Too can't understand why they aren't being showered with love and kisses, and the noise starts.
Bean is VERY quiet. I don't keep her in a cage, I don't like caging birds. she has her own bedroom. She never makes a sound in her bedroom, at all. Just chills, plays, looks out of the window and sleeps in 'her' wardrobe. She chats when she is out of her room. If we are talking between us she will join in, but she never screams or shouts. Ever. she talks too but only knows a few words. She is very obedient...and yes I'm using that word for a bird. If she tries to play with something she shouldn't. I just say no, and she immediately drops it and walks away from it. She also comes to call.
I was very strict with Bean as a baby. Ie she wasn't allowed on me unless I gave her permission, nothing worse than a clingy Too. As a result of this she has excellent manners. she is good as gold with strangers, just being very quiet at first, but she will let anyone touch her and pick her up.
I am her favourite person though and she will always come to me over my boyfriend, however she loves him too. He does get in 'trouble' though, where she puts up her feathers and runs around him, pretending to fight with him, but its all show, she has never bitten anyone or even tried to. She is just hilarious.
Her favourite thing to do is go under the duvet, she actually lifts it up so she can get under. and she goes to sleep under there. She also likes to sleep in my arms if I let her. I do the odd day, but not often. I don't have a strict routine with Bean, so she is never left 'waiting' to be let out at he exact same time everyday. This also helps as if your day changes, you don't come back to a stressed destructive, plucking cockatoo.
I usually open Bean's bedroom door at about 8am and she cruises around the house all morning. I'm home all day. She either chills on the bed or comes in the lounge and sits next to me. She is more like a dog than a person.
So long as you don't spoil them, and its tempting, and your strict about personal boundaries...they are called velcro birds for a reason, you will be fine.
As I said Bean is very loving, very quiet, not destructive at all, just a joy to be around.
Good luck if you decide to go ahead! I love Greys too and have just got my second, and have also had Eclectus, but nothing compares to a Too if you want a bird that is much more than a bird.
I will definitely getting another U2 in the near future. I adore them!