The system basically work in this series: a new registration is made in the database, the system sends me an e-mail notifcando a new record.

Do you have any code that ypu've written. So the community can know what you need.
Php code and mysql schema.

Look up PHPMailer, in my experience it really is the best option. You can of course use the php mail() function, however, it does depend on a local mail server, wheras PHPMailer can connect through SMTP. https://github.com/PHPMailer/PHPMailer

Once configured correctly, you can easily make calls to PHPMailer to construct a message. Simply place that code once your database function returns true.

If you doubt is who to know when to send an email, i see two options for you:

  1. Use cron jobs that will run at specific intervals, identify the new records and send the e-mail. This way you can do it easily with PHP but you'll need to have some flag to know if that record was already mailed or not.

  2. Use a trigger on your SQL Server that will run and external command (probably call your PHP mailing page) each time a record is created.

<?php
//query insert new record

//if(//inserted successfully){
    //send email
    if(//email_was_sent){
        //inform_user
    }
}
else{

}

?>