Monthly statements are a report, a sending profile and a job queue entry.
Tell Me: Customer Statement report. Set the date filters (%month tokens, tip 8), choose Print, Email or both per customer from their Document Layouts (customer card → Document Layouts: statement, with the email address to use). Use Schedule on the request page to put it on the job queue for the first of every month. Customers who want it printed get it printed; the rest get an email with a PDF; you do nothing.
The same Document Layouts setting per customer is where invoices, credit memos and confirmations get their email address and layout, so set the whole set at once when onboarding a customer.