You need to check out the Tails project (https://tails.boum.org/) which is a version of Debian I believe tailored to be completely anonymous. The browser uses TOR by default, I don't even know if you can disable it. Lots of other goodies too, including making browser fingerprints pretty meaningless.

Also, I know it's technically kind of bad form but if one wanted to run Tails easily you can use VirtualBox (https://www.virtualbox.org/) to easily fire up a throwaway instance of Tails quickly and easily.