Both handle standard mail settings well.
THUNDERBIRD
- Account Settings > Account Actions > Add Mail Account.
- Enter name, address and password, then click Configure manually.
- Incoming: IMAP, mail.yourdomain.com, port 993, SSL/TLS, normal password.
- Outgoing: SMTP, mail.yourdomain.com, port 465, SSL/TLS, normal password.
- Username on both: the full email address.
- Re-test and finish.
Thunderbird is also the easiest way to archive mail from a mailbox you are closing: connect, then drag folders to Local Folders.
APPLE MAIL
- Mail > Add Account > Other Mail Account.
- Enter name, address and password. It will fail to find settings automatically.
- Enter mail.yourdomain.com for both incoming and outgoing, with the full address as username.
- Once created, Mail > Settings > Accounts > Server Settings. Untick "Automatically manage connection settings" and set the ports explicitly: 993 incoming, 465 outgoing, with authentication set to password.
THE COMMON FAULT ON BOTH
Automatic port management picking an unencrypted port and failing. Set the ports by hand.