A few questions and remarks:

How many teams can sign up?

Will you be using a knockout or a group format?

What is your definition of those "fair" matches you mentioned? Random matchups or something?

You may want to arrange dates for the matches the same way reptile did in his clan tournament: set a date and time yourself, and if any of the players know on beforehand that they can't make it, they can ask to set up a new date and time until everyone's happy. I'm afraid that if you let people arrange this all by themselves, they'll never get around to completing their games. When doing this however, keep the differences in timezones between some players in mind.