Short Overview:

(Note: Change all instances of joeuser@paonia.com with your @paonia.com E-mail address)
POP3 Server: mail.paonia.com
SMTP Server: smtp.paonia.com
Username: joeuser@paonia.com
Password: (stays the same; don't change)
Uncheck Secure Password Authentication/ Never SSL TLS
POP3 Port: 110
SMTP Port: 587 (recommended) or 25 (default)

Thunderbird Screenshots: