The Heathrow Connect is much cheaper than the Express. Ok, so it's not so frequent but it saves quite a lot. I think a booked limo is around £45. Heathrow Express £16.50 one way (although I think you can get around 15% off looking at the Hex promotion thread). Connect is £7.90 one way. The trains go to Paddington so you would need to get either taxi (<£10) or tube (£1.60? with an Oyster card). Tube all the way from Heathrow will take a long time but be the cheapest option.