The best sample for estimating the number of students who bring their lunch to school every day is 80 students selected at random during lunch.
This sample is likely to provide a good representation of the overall student body because it captures students who are in the lunch environment, making it more relevant to the behavior being observed (bringing lunch to school). The other options are either too specific (like only first-year students, Math Club members, or female students) and may not accurately reflect the broader student population's lunch habits.