Transportation from Heathrow to London

I'm sure you will get a variety of responses to this question. If it were me, I would get the Elizabeth Line to Tottenham Court Road and then switch to the Northern line two stops to Charing Cross.

Is your accommodation at Charing Cross or are you aiming to catch a train?
If the former, where are you staying? Some places are just as accessible from Embankment station, which opens up the easy and cheaper route via the Piccadilly and District tubes.

The answers depends on where exactly you are going to.

My family and I normally take the Elizabeth Line from Heathrow into London and then transfer to another Tube line. In your case, you could take the Elizabeth Line to Paddington and then transfer to the Bakerloo Line to Charing Cross.

If you have 4 or more people in your party, or if you have a lot of luggage, a taxi would be slightly more expensive than taking the Tube but a whole lot more convenient. Your call.

Enjoy London.

Penn

I am going to the Clermont Hotel at Charring Cross. Does that impact any of the above suggestions?

I recommend using a planner like CityMapper or TFL to help make efficient use of your time on arrival day. It accounts for how busy the trains are, closures, etc. It will also advise routes that are more efficient than taking the tube. For example, plugging in your specific hotel and a departure time of noon tomorrow gives four options with about the same amount of travel time: Elizabeth line then walking, Elizabeth/Northern lines, Heathrow Express/Bakerloo, and Elizabeth/Bakerloo. If you buy Heathrow Express tickets early (more than 30 days ahead) they're much less expensive.

the Clermont Hotel is in the Strand practically in Charing Cross (note only one "r" in Charing) station. The Bakerloo and Northern lines (both mentioned upthread) are right at the front of the station. Hard to get more convenient. Out of the tube and you're home.

However, if mobility is an issue, Charing Cross - either line - is not step free.