A group of Microsoft Products and technologies used for sharing and managing content, knowledge, and applications.
Hi Harvey,
From your description you would like to know the settings of sharing a SharePoint site. May I confirm with you the three privacy options you mentioned above is referring to the Excel Sharing in SharePoint admin center? If so, I think you can setup the external setting in admin center in this way if there are no special requirements as below. You can set the permission level to New and existing guests and check the option Guest must sign in using the same account to which sharing invitations are sent.
To sharing a modern SharePoint site to external user, you can open the modern site and go to Site permissions > Advance site permissions > select a group > Click New to add an external user.
To share a classic site, you need to go to SharePoint admin center, select the classic site > Sharing > check the option New and existing guests and save it. Then you can go to the classic site and click share button to share the site.
For your additional references to understanding SharePoint permissions and external sharing.
Understanding permission levels in SharePoint
Best regards,
Dihao