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