The best sample for estimating the number of students who bring their lunch to school every day would be 80 students selected at random during lunch.
This sample is more representative of the entire student population because it includes a broader range of students from different grades and backgrounds, rather than being limited to a specific group (like Math Club members or only first-year or female students). By selecting students during lunch, you are also likely to capture those who are actually eating at school, which is relevant to the question of who brings their lunch.