Hey there!
Welcome to the forum
In reading your post, it sounds to me as if you don't have a whole lot of experience in training/taming birds. They are UNIQUE and GCC's ESPECIALLY can be mega challenging to tame.
HOWEVER...that being said, other GCC's can or will tame down in no time at all and be your best cuddle bug bird ever.
How can you tell which one will be the cuddle bug? What's the guarantee?? Well...no way to tell...no guarantee's.
I can tell you from our experience with our Franklin...who is now 2 1/2 years old...that if he hadn't been tame when we purchased him...we would have been more than likely...miserable and highly frustrated with sore hands from being bitten so much!
His bite packs a punch, he can be extremely aggressive and for no apparent reason other than he is just an extremely independent boy who likes to call the shots! LOLOL
He's highly....and do mean HIGHLY active...I describe him as being ADHD with a splash of Bi-polar...and I don't mean ANY disrespect toward anyone. But that's our Franklin in a nutshell.
Even though he was hand tame and had an excellent foundation on him when we got him...our first year was still challenging at times, having to be consistent, set the rules...so to speak...and stand by them.
I can't imagine trying to tame him down at his age now, had he not ever been handled.
You mentioned having children who would like to at least hold the bird....then it's my opinion that it's really in your best interest to pay the extra money and get a hand tamed baby....with a good solid hand tamed foundation.
I don't think you'll regret it...for a family bird.
I think the untamed 3 year old would be a great project for someone...for sure...but I wouldn't advise for a family project.
Then again...going back to no guarantees...she might be the PERFECT bird for you.
Good Luck in what ever you decide.
On a side note: Conures have seemed to explode in popularity in the last few years...and they are definitely FUN birds. But read in the posts on this forum...almost every other post is about Biting issues...severe biting issues...aggressiveness...
Good Luck with what ever you decide to do. And DO keep us posted!
Toni