Using the www.tfl.gov.uk web site it looks like the best way to get there is either Express or Connect then tube over to Victoria. Both routes take about an hour according the site but one costs twice as much. Do I understand it correctly?
The Connect is cheaper than the Express because it makes a few stops along the way, and also doesn't operate as frequently...it's deigned to transport airport workers. If it were me I would take the Tube to Earls Court and transfer to to District/Circle Line three stops away to Victoria Station. With the Express or Connect you will have to wait in line to purchase underground tickets, defeating any time savings....also Paddington (where the Express/Connect terminate) station is farther away. Tube will be cheaper than both.
I'd also suggest taking the tube. I'd recommend that you transfer to the District Line at either Hammersmith or Barons Court as at these stations you just walk across the platform to transfer. If you transfer at Earls Court you have to change to a platform on another level.
I just did this last week, took Tube to Hammersmith, walked across platform (no steps) and caught District line to Victoria. You will have to walk up some steps at Victoria so hopefully you pack light. Not sure of price as I used my Oyster card.
Thank Elaine. How long did it take you?
Why not take the National Express bus? It goes from the Heathrow Coach Station directly to Victoria coach station. No changes to the tube, no having to wrangle your bags because they get stored in the belly of the bus. I haven't done this in about a year or so, so I don't recall the fare, but as I recall it is a bit more than the tube and a lot less than either train to Paddington. The biggest advantage, besides money, is that you can simply take your bags over to the coach station on an airport trolley, buy your ticket at the station, hop on board, and relax till you get to Victoria station. Easy peasy.