To take advantage of the best prices you will need to prove you are a leisure traveller, on the way to the airport, so you will need to provide either yr flight details or your holiday booking reference. I don't think you will need to give this when you arrive at the station but you may be asked to provide them on your travels from greenwich station to the airport.
Going to the airport on the train is great, you can sleep, read (even at night), play a game, or just stare out of the window... The other caveat to buying these cheap train tickets from greenwich station to the airport is that there must be at least two grown ups travelling together. But another great advantage is that children go free. All kids under 5 go free, and then one child over five but under 16 per adult travelling by train to stansted airport.
make sure you leave enough time to get to stansted airport early enough to eat, shop etc, so check the times of trains from the station before you go. If you end up with time to kill at the airport you can always read a book or play travel scrabble again! As you have bought yr train ticket in advance, you don't need to fret about the opening times of the station.
Or maybe you meant