Gmail – Mozilla Thunderbird “Get Mail” doesn’t get all the mail from the beginning

I would think category:primary would work. You'd put that in the "Has the words" field.

(I just tried it, and it seems to work.)

If that doesn't work for you, there's only a few categories, so you could always try negation.

-category:updates, -category:social, -category:forums, -category:promotions 

In other words, not one of the other categories.

You would need to write some sort of regex to extract that string from the message.

var threads = GmailApp.getInboxThreads();

for (var t in threads) {

  var messages = threads[t].getMessages[];
  var text = messages[0].getPlainBody();

  var matches = /From:(.*?)<(.*?)>/gi.exec(text);
  if (matches) 
      Logger.log(matches[1] + " :: " + matches[2]);

}