the High School Starleague, we're a varsity-level tournament between high schools in North America. We have weekly matches for each HS in LoL/Dota2/Hearthstone/SC2, and even stream some of the matches. Last years winners, Cerritos High School (they also participated in the Challenger Series qualifiers) took home $7,500 in scholarships at our grand finals.
So, there's essentially two types of clubs focuses a club can take:
1) Competitive: directed around self-improvement, learning; these types of clubs take on similar traits to "varsity-level" sports clubs.
2) Community: fostering student growth in social skills through interest-based leadership. Many clubs take a combined approach, which works well, although your administration may feel that the club is overextending themselves.
I'm assuming you're going to be speaking directly with your administration. If so, there's a few things that administrative teams at other high schools loved seeing:
