If you really wanna pay for one of the most expensive rail journeys in the UK, Heathrow Express is where it's at. If not, Heathrow Connect or the Piccadilly Line (tube) are much cheaper.
If you have an annual travel card, show them your Gold Card when buying a ticket - 33% off the usual price (after 9:30am I think). Not available from the ticket machines though.
Only expensive if your time isn't worth the quick commute into London. Tube/buses can be difficult w/suitcases & for the single traveler, this works a treat.
Buy the ticket before boarding as they charge extra otherwise. You can use railcards on Heathrow express at off peak times including gold card to save 33%