Usually, free software comes with privacy and privacy comes with free software, so the first thing that you should look for is the distribution's policies on free software. Distributions like Debian and Fedora, for example, have a strong commitment to free software (see Debian's Social Contract[0] and Fedora's licensing guidelines[1]) and are not going to spy on you or put ads on your system. The Free Software Foundation maintains a list of distributions that contain only free software[2], and these distributions aren't going to collect your data and send it to third parties without your consent either.

Ubuntu, on the other hand, does not have such a commitment to free software, and has included Amazon ads in the Unity dash in the past.

[0]: https://www.debian.org/social_contract

[1]: https://fedoraproject.org/wiki/Licensing:Main

[2]: https://gnu.org/distros/free-distros.html