Group planning

Hello, 

I am new to Planner, and am looking for help. It is also possible that Project would be a better app, I am unsure. 

We have a team of 23 people, and I want to assign 5 tasks with deadlines that all 23 people have to do. In my first attempt, via Teams, I used Tasks by Planner, which looked okay, but once 1 person marked the task complete, it was marked complete for everyone. 

I want to use this to track who specifically has completed each task. Sometimes the task will be simply a "check", and other times it will be submitting a file. 

Please advise on the best app, and how to set it up.