Norton removal tool is a must in my book as well.
After that, CCleaner for registry scan just to be on the safe side.
I am not a fan of Norton myself and if I ever recommend Norton, it would be NAV. What bothers me the most its their file reputation that is not always accurate. But then again it can be overcome if I choose to.
On a side note: Difference between 360 and NIS is not only the pc tune up.
360 also includes backup.
link: http://us.norton.com/comparison/promo