I mailed my paper claim in yesterday. It only asked your name, address, and birth year. Nothing else.
It looks like, if your goals are a balance between receiving the settlement, privacy, and effort, the PDF (probably [2] if no minors were involved) is the way to go.
[1] https://www.equifaxbreachsettlement.com/file-a-claim
[2] https://www.equifaxbreachsettlement.com/admin/services/conne...
[3] https://www.equifaxbreachsettlement.com/admin/services/conne...
[0]: https://www.equifaxbreachsettlement.com/admin/services/conne...
[1]: https://www.equifaxbreachsettlement.com/admin/services/conne...
Straight forward.