The problem with third party candidates in this country is that they get almost zero support. They get no electoral college votes whatsoever. The best bet in this country is usually to try and get change within the two existing parties.
An example of that is The Tea Party's influence on the 2010 midterms. Love them or hate them, you couldn't ignore them. They influenced policy of the Republican party. That's the best strategy for any group that wants their voices heard.