Just a word of warning. The queues to use the ticket machines at Gatwick are a disgrace and part of the reason behind this is the sheer complexity of the fare structures.

IIRC, once you hit the button marked "London" it then comes back with three pages worth of results.

So, if you do see a roving ticket seller in the airport, I would be sorely tempted just to buy from them, even if it does mean buying the slightly more expensive Gatwick Express/any train ticket.