So I’m the co-chair of a 10s rugby tournament this weekend, and we’re making the brackets tonight (the big ones that are posted at the HQ tent).
There’s going to be four brackets:
Men
Women
College Men
High School Girls
However, it’s actually a “Men’s Club”, and a “Women’s Club”.
What about the others? Should it be a “Men’s College” or a “College Men’s” bracket?
“High School Girls’”, or “Girl’s High School”.
Or should we just write it as the way I did in the original list.
I’m pretty sure I know the answer, but the other co-chair said “go ask your friend Ceicel Adams”
*I put the apostrophe in the wrong place in the title on purpose. I wanted to drag some nitpickers in here. 
I’d go with what you’ve written above.
High School Girls describes a category of people that are girls in high school.
Girl’s High School describes a school belonging to **a ** girl, or perhaps named after a person named Girl.
Girls’ High School describes a school belonging to, or attended by, multiple young females.
Perhaps if she’s home-schooled.
Myself, I would hyphenate “high school” if it appears before “girls”: High-school girls, but a girls’ high school.
Can you please elaborate? I don’t understand why.
Could also describe a category of girls in school using illicit drugs. 
In that context, “high-school” is a compound adjective. “High School Girls” describes school girls who have partaken of certain substances.
High school girls: school girls who have been using drugs.
High-school girls: girls nearing the completion of their secondary education.
The hyphen shows that the first adjective modifies the word that is bound to it by the hyphen, not the main noun in the phrase.
Correct. “High school” is being used as a single entity modifying girls but – the important part – placed BEFORE what it’s modifying. “High-school girls,” but “Girls who are in high school.”
Same reason I write “He is a well-known author,” but “The author is well known.”