Heathrow Express and Black Cab Combo

If you have not already done so, look at the Heathrow Express pricing structure. The farther out you buy, the cheaper the price.

I don't see anything obviously wrong with your plan. The worst that happens is that you have a slow trip through traffic from Paddington to your hotel. But you'll be sitting down and looking out at London, and with three of you to share the cost it shouldn't be a bad deal at all.

I once shared a cab with a fellow train passenger from our arrival station, Paddington, to Victoria Station, which was her departure station for her onward trip and very close to my London hotel. It didn't take very long; I had my luggage with me, and it was worth every pound of the shared fare, for the convenience and security vs. trying to wrangle the bags on the Tube.

(You've probably discovered that the best fares for the Heathrow Express are 90+ days before your date of travel. I just bought my HEX tickets online for my early November trip; I calendared a date about 95 days before my arrival so I wouldn't forget and miss the low fare.)

Another option is to take a prebooked car (called a minicab in Brit-speak) right from Heathrow to your hotel. This is much cheaper than a black cab from the airport, and you get door-to-door service. For 3 people, the cost per person would be quite reasonable.

I have no personal experience, but three companies that are often mentioned are Just Airport https://justairports.com/, Simply Airports http://www.simplyairports.co.uk/, and Blackberry Cars http://www.blackberrycars.com/. For each of them, you can go to their websites and put in your particulars, and get a price quote. Note that Just Airports has a substantial discount for cash (don't know about the other two).

Your way is fine. Probably the most expensive. But not necessarily the fastest as you will see in London traffic.

I would take the tube but I travel light. If you have lots of luggage, and there are three of you, a prebooked car service, or Uber, would be basically "door to door."

The ones mentioned previously are well on own. You could also contact your hotel to see if they use any particular service and the cost.

We want to maximize our time there, but also not spend a fortune.

If you want to avoid the Tube completely, here are 2 ideas.

1. Take the Heathrow Express (HEX) to Paddington and get a black cab. When you buy HEX tickets at least 90 days in advance, you'll get the cheapest fare of £12.10 which is not much more than the Heathrow Connect (to be called TFL Rail in December). Then with 3 of you in a black cab from Paddington, you can split their exorbitant pricing to your hotel 3 ways making it more affordable. This will give you the greatest flexibility too. Keep in mind in the black cabs, you will be sitting in traffic as the meter keeps going up and up.

2. Take Simply Airports or Just Airports car service from Heathrow to your hotel. By the time you three are done with immigration, rush hour traffic into London is long gone. There will be traffic within London so keep that in mind. Sharing the cost makes it even that much cheaper; it's lightyears cheaper than black cabs too as there is no meter.