Is there a way to schedule a weekly report of a campaign that shows only net new leads/member of that campaign?
Of course, run a People Performance Report (aka Lead Performance Report). The setup of the report will include leads created "in the past 7 days" and the smart list of the report will include "member of program". The resulting list will show all leads who have been created in the past 7 days and who are members of the program indicated. Then you can subscribe to this report via the "Subscription" tab and select the day of the week you would like the report emailed to you.
Does it only show createds? what if someone is updated and joined the program in that time span?
Program performance report. You can use leads acquired/created column.
Drawback: You can not exclude internal/test traffic.