Well, they don't really come in "mean". When they bite, there is a reason. He's young, so it's unlikely it's a deeply ingrained behavior. It could be that he's getting a little afraid or a little over-stimulated. It could be that he's trying to preen you back and getting carried away. It could be that he has learned biting is a good way to either get you to stop interacting when he's had enough (in which case you need to learn when he's getting there and put him in his cage or on a play-stand sooner) or else he's learned when he does it, you sing and dance... drama of any kind can be highly rewarding to a bird, especially a GCC. He doesn't necessarily realize he's hurting you.
I'd suggest slowing down a bit. Handle him less. Stop before he bites. Find behaviors you like and reward those. Put him away on a good note. Feed him treats when he's been sweet. Handle him less and talk to him more.
I agree with avoiding the bite as much as possible. It's much easier than not reacting, I think it is very hard to avoid producing any reaction. At best you wind up freezing, which is still a reaction. And those little beaks can be quite painful, really.
Punishment is tricky and probably best avoided. Physical punishment is dangerous and yelling or even giving time-outs can unintentionally reward and reinforce the behavior. I've had much better luck trying to catch and reward behavior I like, "Oh what a good gentle bird!" than trying to discourage behavior I don't like.
GCC are actually not easy birds IMO. They are small, so they often are selected as first birds, but our GCC is way more difficult than our Cape Parrot. So give yourself some time to figure him out. Slow down and don't expect him to always be cuddly on your terms... read about parrots... target and trick training is probably a good way to go, but may require more discipline than you had in mind.