The following article provides suggestions and guidance for selecting on-site badge printers.
iOS devices require AirPrint-certified printers: https://support.apple.com/en-us/HT201311
Note: Unlike Android, no additional work is needed to custom fit any printer not found on the list above.
Cloud-ready printers are the easiest printers to connect with and use: https://www.google.com/cloudprint/learn/printers/
Any printer not on the list can be configured to work with your Android phone, but this will require additional manual work.
Within Certain's offices, we recommend and use for validation and acceptance testing any Brother QL series printer (QL-700, QL-710W, QL-720NW, QL-800, and QL-810W). For more details, please see the file attached to this article.