Heathrow Express, Connect, Piccadilly Line?

Sorry, you can have convenient, or you can have cheap, but not both. The most affordable will be the tube, but the Piccadilly line doesn't go to Marble Arch. The easiest route would probably be to go to Holborn to change to the Central line and backtrack. It'll take around an hour, I would think. Go here for maps and times: http://www.tfl.gov.uk/ I think the fare is currently 5 GBP/person, but it may be less on an Oyster or Travelcard (do a search on this board for info on them). However, you say "family". The most convenient method would be shuttle service, using something like http://www.justairports.com/ and with enough people this might well be cheaper than either of the main line trains.

Good advice from Kathy above. My own recommendation would be the Connect, then a taxi from Paddington to your hotel. A taxi shared among 3 or 4 for that short distance will be very reasonable per person, and given that you will be jet-lagged in an unfamiliar city with luggage, I think the Tube will be an unpleasant way for you to arrive in London. And if your arrival coincides with rush hour, well, the Central Line will be an experience for sure.

Kathy, Roe, Thank you so much for your advice and quick response. The 3 couples are flying different airlines and landing at different times, so I think the shuttle is out of the question. So either the Heathrow Express and Tube to hotel or the Heathrow Connect and taxi to hotel are the best options. I found a discount of 33% of AMEX customers for the Heathrow Express.

No don't have a 50% off code. Yes a "single" ticket is one way, "return" roundtrip. Underground is the cheapest but most time consuming route into London. Does not go directly to Marble Arch from Heathrow. Takes about an hour to get into London. 20 stops along the route into London. Piccadilly line from Heathrow to the Green Park station, exit, take the Jubilee Line to Bond Street, change again to the Central Line to Marble Arch. Heathrow Connect is cheaper than the Heathrow Express but takes longer (15 minutes) and is less frequent than the Heathrow Express. Just be certain to double check which Terminal you are arriving at in Heathrow. If it's 4 or 5 you'll need to use their free shuttle to Heathrow Central beneath Terminals 1 & 3 where the Connect departs from.
Once you get to Paddington, take Roe's advice and enjoy a cab ride.

@Candy - how different are the arrival times? It might be worth having the first arrivals eat breakfast at Heathrow and wait for the others.

Thanks for all this helpful information everyone. The arrival times are hours apart...and that's not guaranteed with the possible delays, so I don't think it's wise to count on waiting for everyone to meet up. Also two couple are coming from the east coast while one is coming from the west coast. How much does a taxi cost?

Thanks all very much! I now have a plan! Happy travelling.

The changes from the Piccadilly Line at Holborn or Green Park to reach the Oxford St area are both pretty inconvenient with long walks and/or escalators up and down. If you're going from Heathrow to Marble Arch by tube my strong recommendation would be to get the Piccadilly Line to Hyde Park Corner, leave the tube there and get a bus up Park Lane to Marble Arch - there are many different routes.

According to worldtaximeter.com, the cost of a taxi from Paddington to Marble Arch would be 4 pounds. With tip, say $10. While I have never taken that exact taxi route, I have taken a taxi from Paddington to Euston, and it was about that price, so I think that is a decent estimate. 4 pounds really is quite reasonable all things considered.