You may take narita express from airport. But at the Shinjuku station, you need to go staircases with your suitcases. Not so convenient but no traffic jam. Airport Bus can be reached to the entrance of the hotel. When I left from Japan, I took airport bus and no traffic jam.
Disney land, some hotel eg Keio Hotel had booking services. You may check. I lived at Haytt Hotel and no such services. Only take JR to Disney and quite fast.