Ubuntu is the best for me, try it Ubuntu Studio, with lots of multimedia software.
Ubuntu Studios comes with a lot of multimedia software, but it doesn't come with the restricted codecs that the original poster wants for the reason that Canonical is a legal entity that can't provide these codecs for free.
Other distros like Mint that do have these codecs preinstalled are community distros with no corporate entity, and they are based in a foreign country that don't enforce these intellectual copyright protection.
That's why you'll never see Canonical, Red Hat, and Novell include these codecs out of the box. (They would be sued if they did).
If you feel that you have a moral obligation to be 100% legal, you could buy the license to use these codecs.
DVD Playback Here: