I love recurring billing! You should set up a merchant account and then use a payment terminal. I use my local bank and authorize.net, If you have not yet set up a merchant account then you should opt for square ( square.com ) they will send you off a card reader that you can use with you smart phone for free and the account is free as well.
If I didn't have a merchant account set up yet I would take down all of the clients info, along with a billing cycle date and other details, and store it in a file somewhere safe. Then when his date came on the calendar pull out your square app and bill him and send him an email receipt.
Here is an extra tip for you as well that could save you several hundred to thousands.... make sure you have the client sign an initial receipt that states in the fine print that they are going to be auto billed every month until they cancel. This way if they try and chargeback (and believe me even if you do incredible work and have exceptional customer service you will still get chargebacks when you start dealing in volume) they will not be win a dispute with the credit card company.