To the target audience of the library?

Outlook.com as it's the simplest to use. Their immediate concern is their livelihood so they need a free email account and not have to think about anything else including its lifetime.

To a techie audience?

ProtonMail, FastMail, Tutanota, GMail, Postfix...

Gmail sounds like an odd recommendation as a replacement for Gmail.

Losing a password would lock them out of all previous emails but they would be able resume use of the account