WiFi isn't charged to you. Data is. Data is through the carrier/service provider. WiFi is accessed through either your home WiFi, other people you know who have WiFi (if they let you) or open WiFi in some public places, like say libraries.
So you don't pay for WiFi access (well not through the phone's carrier/service provider), you pay for data access. You can actually turn off data and use only WiFi to connect. The only time this would be an issue is in sending an MMS message (multimedia message) through your messaging app (not messenger). If you were sending it with a photo, or other item attached, then it would require data. Most anything else can be done via WiFi.