President-elect Donald J. Trump on Sunday chose Reince Priebus, the chairman of the Republican National Committee and a loyal campaign adviser, to be his White House chief of staff, turning to a Washington insider whose friendship with the House speaker, Paul D. Ryan, could help secure early legislative victories. In selecting Mr. Priebus, the president-elect passed over Stephen K. Bannon, the right-wing media mogul who oversaw his presidential campaign. If Mr. Trump had appointed Mr. Bannon, a fierce critic of the Republican establishment, it would have demonstrated a continued disdain for a party that Mr. Trump fought throughout his campaign. Mr. Trump’s choice is certain to anger some of his most conservative supporters, many of whom expect him to battle the Washington establishment over issues like taxes, immigration, trade, health care and the environment. They view Mr. Priebus as a deal maker who will be too eager to push the new president toward compromise.