There are many lodging choices in London and several factors to consider before deciding which place to sleep.
The cost to get from Heathrow to your London hotel can be substantial.
Here's one money-saving tip to consider:
If you choose a hotel that is reasonably close to a Piccadilly line tube station ("reasonably near" considering the distance you'll have to pull/carry your baggage), then note that it's a straight shot from Heathrow into those parts of the city served by the Piccadilly line. If your hotel is reasonably close to a Piccadilly line tube station, you won't have to transfer to another line, and it will only cost you about £5.7/person.
Note that stairs and lack of lifts (elevators) or escalators are issues to consider, some Tube stations have them and some have only stairs.
The £5.7/person can be a significant savings over other alternatives, depending on your circumstances.