I think FOX is basically in terms of idealogy is basically Mainstream or Reform Conservatism except for Hannity who is on the fringe on the right on the political spectrum. Hannity maybe not be as far-right as his friend radio host Mark Levin but he still is pretty right wing. Hannity is basically follows "Tea Party Idealogy" even if "The Tea Party" fad went passe a few years ago.
FOX is
Reform Conservatism? Maybe there's some of that among a few people there, but overall it's quite the opposite. Their market strategy is to do everything possible to keep people comfortable in their intellectual and political habits and not reforming anything because that involves critical self-reflection, which they believe is too much to ask of the common man. Hannity is more a shill for the GOP than for any ideology, aside from feel-good apple pie jingoist nationalism. He'll get 100% behind Guiliani or Trump if he believes that's the way the wind is blowing.