johnny & lethoso (and also Gangrell if you read this!) - there's a great parrot forum
here if you're interested - a nice bunch of people who like to talk about their parrots. There are a few breeders there, and a student avian vet, so it's also a good source of advice on all aspects of parrot keeping.
lethoso - I have a Senegal parrot. He is wonderful, but typical of the species - feisty, aggressive, nervous, and hates everyone but me. I don't know anything about King Parrots because they're not common in the UK, but I know that both Alexandrines and Quakers make excellent pets.
King Parrots - what I've heard is that they don't make such good pets because they have a tendency to become untame when they reach maturity. I don't know how true that is, there is little experience of keeping them in captivity in the UK, but they tend to be viewed as aviary birds rather than pets.
Alexandrines - don't tend to bond too strongly to one person because in the wild they take a new mate each year, so are less jealous than other parrots. Can be noisy, but are generally quieter than other ringnecks. Need handling every day or they will become untame.
Quakers - absolutely adorable little birds, when I was after a parrot it was a toss up between a Quaker or a Sennie. They are highly intelligent and good talkers - they need to be kept entertained, and some of them even start talking before they are weaned. They make strange noises which some people (even parrot people) find unpleasant, so it would be a good idea to go and listen to some before taking the plunge - personally the noises they make don't bother me, but it's a personal thing. Don't get one if you're ever considering moving to the US because they're banned in many states. They can become cage territorial, but training can minimise this, and you should train them to step up onto a dowel perch just in case. Most of them like to sleep lying down in a cardboard box on the floor of the cage rather than on the perch - but avoid those happy hut things or fabric nests because I've heard horror stories about birds chewing them and hanging themselves in the holes they've made.
Personally out of those 3, I would go for the Quaker, but I suggest you go to the forum I posted a link to and ask for advice there - there are bound to be people on that site who have personal experience of all three species.
About your territorial budgie - if you move his toys and perches around regularly, he won't view it as 'his' cage so much, and that may help. My mum's budgie is like that - bites the hell out of you if you put your hand in his cage, but is sweet as anything outside it.