mail.yourdomain.com for both POP and SMTP. Use full email address, user@yourdomain.com, to login.

You need to add
Mail.Helo = "yourdomain mail"
That line will transmit the handshake header to keep it out of spam/bulk email boxes.

You must use full email, admin@yourdomain.com.

First, goto http://mail.yourdomain.com:8383, then login using admin@yourdomain.com as the email, and account password. Select User Administration from the drop down list. When come to a new page, click 'Add' and enter the information.

Set Mail = Server.CreateObject("Persits.MailSender")
Mail.Host = "mail.yourdomain.com"
Mail.From = "user@yourdomain.com"
Mail.Username = "user@yourdomain.com"
Mail.Password = "password"
Mail.FromName = "Your Name"
Mail.AddAddress "to@otherdomain.com"
Mail.AddBCC "cc@otherdomain.com"
Mail.Subject = "Subject of the email"
Mail.Body = "Body of the email"
On error resume next
Mail.Send
set Mail = nothing
If Err <> 0 Then
    Response.Write "Error when trying to send mail"
end if

This happens because your domain is being or not transferred. If you already changed the DNS, please allow 2-3 days for the transfer to complete.

It's possible that your ISP block external SMTP and require you to use their SMTP server to control spamming. Please check with them.