The cheapest way to sit at center ice for a Capitals game is to choose seats in the 400 level mezzanine sections. Despite being the farthest seats from the playing surface, they do offer unobstructed views of the action and equitable views of both ends of the ice.
With roughly 15 rows in every section, none of the seats come with an incredibly long walk up the stairs. But you'll still want to be as close to row 3 as possible. Not only will you have closer views than the fans sitting in higher rows, you'll be closer to the section tunnel and the concourse and its amenities.