From your OLD computer...
Copy your ENTIRE iTunes FOLDER to an External Drive... and then from the External Drive to your New Computer..
I have just transferred my library from my old laptop to my new laptop
Did you follow All the steps as described here...?
Full Details Here > http://support.apple.com/kb/HT1751
There are a number of methods described on this page which you can use to copy your content between computers : http://support.apple.com/kb/HT4527
The page specifically refers to music, but I've used the 'home sharing' method to copy films, apps etc as well as music between computers.
You should be able to use a USB stick, assuming that its capacity is high enough for your library