If the old computer goes to junk, you might as well just move the old disk over to the new PC and leave it there, no copying needed and the extra space won't hurt. Plus this way you don't have to worry about securely deleting what's on the old disk because you don't throw it away.
If you connect 2 computers together via network cable, that'll prolly be the 'fastest'. I do it at work every day.. 6 times a day in fact as we're upgrading machines and we copy profiles and stuff that way.
Just set them both up with static IP addresses and copy the data that way. At 100Mbit you should be able to copy 10GB in less than 30 mins or so.