Rock paper scissors
Starting with the monosyllabic word allows for a forceful and strong beginning which readily captures attention and encourages the other person to focus on the contest at hand. Additionally, since "rock" and "paper" are not usually paired together and do not share many semantic or lexical fields, it is clear that the formulaic chant of a rock paper scissors contest is underway. By contrast, paper and scissors are often paired together in a wide variety of contests which, if "paper scissors rock" is used, can lead to confusion about whether a game is underway or a simple list is being spoken for another purpose entirely. This confusion inevitably disadvantages the person who did not issue the game challenge thereby contributing to the effect where a more confident person has greater chance of success regardless of their ability. Is this really a divide that we want to continue entrenching within society? If so, feel free to use that phrasing. But those of us who would rather reduce the divides in our society and form a more level playing field will always choose "rock paper scissors". It is that simple.