I tend to go for the "not iconic" movie scores. If the music is too well known, it pulls the players out of the situation.
Go-to composers: Yuki Kajiura (.hack//, Noir), Yoko Kanno (Escaflowne, Ghost in the Shell, Cowboy Bebop, Macross Plus, Macross Frontier), Sawano Hiroyuki (Guilty Crown, Kill la Kill, Attack on Titan, Kabaneri of the Iron Fortress), Taku Iwasaki (Read or Die! Ruroni Kenshin, Witch Hunter Robin), Keiji Inai (Is it Wrong to Pick Up Girls in a Dungeon?, Heavy Object, Alderamin of the Sky)