I was in the same boat – I found I was able to use the system defaults by simply not trying to set the ‘from’ address and other header information.
$recipient = '[email protected]';
$subject = 'my subject';
$message = 'my message';
wp_mail( $recipient, $subject, $message );
That being said, if your SMTP provider allows altering the ‘From’ information (for example) then it would be nice to know how to customize this by loading the defaults and then altering, but I haven’t been able to find out how to load the defaults.