If you don't already know then I would say the process should start with the debate for who first.
I would recommend, however, that it be done in an unbiased, non-partisan environment. Stay away from any politics, dividing topics, ideals or 'isms'. Make all news about it sound like each group simply found the movement and started to join in without any alliances.
Perhaps start a web site for just this purpose with no traces to any group. We want membership across the board because it's about the facts leading to the overall 'winner', not who gets credit. By the time the 'contest'(ha!) is over, there will be lots of awareness to shift toward the actual boycott.
The first step may be to define the characteristics of what company we should be looking for. This really should include that the company be vulnerable to such an act. I doubt ones like Monsanto would count until the numbers were there.