Hello! I think starting a school newspaper is a GREAT idea!
When I taught in Upstate NY, I started one for our K-6 school. I ran it as an afterschool club for 5th and 6th graders.
During the first meeting, we discussed what our newspaper should be called: "The South Seneca Times".
Then we looked at other newspapers and talked about what we wanted to include in ours- school related stories for all grades, sporting events, clubs, happy grams, comics, teacher interview, student stories & poems, word search, and some type of puzzle.
Then, students signed-up to "cover/report" on what they thought would be of interest to them and other students- (school lunch, a new student, field trips, class projects, etc..
In the beginning, we meet every week or twice a week so that I could make sure the students knew the difference between a newspaper story (5 W's, 1 H) verse is a personal story. Once students knew how to write in newspaper form, we meet twice to three times a month. The first session would be to brainstorm story ideas. The second one to hand in stories and have editors read them over (The first year I selected students I knew who could handle being an editor. Years afterward, I would have a 6th grader who was a reporter the year before). The third session was to put the paper together (layout).
We made the paper using Microsoft Publisher (newsletter format).
The paper came out about once a month. We copied it in our main office one year and the next years I had a company donate funds to cover the copying cost. For grades 3, 4, 5, and 6 each student got a paper. For grades K, 1, 2 we copied a class set for the grade level to share.
If students or teachers wanted a student story/poem publisher who was not in the club, we would always find a way to include it, especially for the younger kids.
I hope these helps! Good luck!