Memento is probably Christopher Nolan's best film, and certainly his most character-driven one. Guy Pearce plays a man named Leonard, who has anterograde amnesia, meaning that he can't remember anything for more than a few minutes. Two men raped and murdered his wife and caused the injury that gave him his amnesia, and he's out for revenge.
Pearce, Moss, and Pantoliano all give performances that feel naturalistic and at times, awkward, although I believe it was done on purpose.
However, the film does not start with the journey, but rather the end. Within the first scene, Leonard has shot a man in the face. Then, the narrative progresses backwards from this point, while also starting at the beginning, with the two storylines meeting up in the middle.