That is a 64 bit CPU, so you can use Netrunner from the DVD. Tails and Gentoo, also on the DVD, would work with your hardware but Gentoo is for more experienced users. Tails is a security focussed distro, but is based on standard software so may also be suitable for you.
Try either of Tails or Netrunner, if you don't like it try the other one.
"Insanity: doing the same thing over and over again and expecting different results." (Albert Einstein)