To the author’s limited knowledge there is no Atheist Political Party. Atheists hold a wide range of different political opinions. Atheists agree only that there is no evidence for the existence of God. Atheists don’t all necessarily agree about politics.
Atheists tend to support Liberal or Social Democrat parties. Atheists are rarely politically conservative because conservatives are traditional. Traditional people tend to support Christianity or some other traditional religion. Political liberals are in favour of helping minorities that face discrimination. Atheists sometimes face discrimination and therefore tend to favor political groups that would protect them.
Libertarian political parties, which are considered very politically conservative by anti-capitalist liberals and social democrats, have a large number,if not majority, of members being atheist. Objectivism, also incorrectly considered very conservative by liberal types due to it's moral support of capitalism and rejection of pacifism, holds that there are no gods, or any other form of mysticism in the universe. Objectivists in the USA are often divided between voting republican (conservative) or democrat (less conservative).
Liberal minded atheists might argue further that atheists support liberal and social democrat causes because they follow the scientific method and focus on improving conditions in this world (as all political parties claim). In their opinion liberal and social democrat policies are better at improving life here. Liberal minded atheists might also argue that countries like Denmark and the rest of Scandinavia are better than the United States at making their people happy despite lower living standards, denser populations and problematic Northern European climates.
An atheist ruler would not feel that he has a God given imperative to pursue certain policies regardless of evidence. Such policies as banning religious advertising or evangelizing would raise free speech issues though there may be a case for limiting the money people are allowed to spend on religious or freethought advertising. Any limit would have to cover both to ensure fairness.
Religious indoctrination of children before they are old enough to think critically is an issue for many atheists. Many atheists believe that frightening children about Hell is a form of child abuse and should be illegal.