As far as coaching goes, Joe Gibbs was terrific at getting the most out of his quarterbacks. He's the only NFL coach to win Super Bowls with three different QBs; Joe Theisman, Mark Rypien and Doug Williams. He went to the playoffs with six different quarterbacks. Theisman has gotten a lot of press, but that was like Don Meredith, nobody would remember him if he hadn't gotten into media after his playing days (and of course, the wicked leg break that ended his career.)
I don't have anything against Shanahan, but he was .500 over his last three years in Denver and I can't see Snyder giving him a lot of time to build a team. That's been Washington's problem ever since Snyder bought the team. You can't just keep blowing things up and starting over.