The first payment will be billed immediately. Your plan will automatically renew on the 1st of the month following the last delivery of your current plan (do not worry, you can cancel the upcoming renewal at any time).
As long as you sign up before the 20th/21st (10 days before the last day of the month) 4pm Pacific Time, you will receive the box for the current month. For example, if you sign up for a monthly plan (pay every month) BEFORE the cut-off date/time for the April Box (April 20th 4pm Pacific Time) you will receive the April Box and your next renewal date would be on May 1st. If you sign up AFTER, then your first box would be the May Box (shipped on/around May 23rd) and your subsequent renewal billing date would be June 1st.