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.

We are going to Paddington via the Heathrow Express. Although quite a bit more expensive when you purchase at the last minute, if you purchase well in advance it is only £10, which is just about the same as the Elizabeth line (I think actually a little cheaper), and it is much faster (only 15 minutes). Of course, then you will have to purchase again to get on the tube to Charing Cross, so that extra cost could factor in.
Since we are going to Paddington and then may catch a cab, it was the best choice for us.

Whilst it is true that a £10 advance ticket on the HEX to Paddington is cheaper than the Elizabeth line which is £15.50, the HEX ticket does not count for the TFL daily cap for zones 1-6, whereas the Elizabeth Line does. The 1-6 cap is £16.30 so taking the Elizabeth Line means that any other TFL journeys on the same day will cost just 80p - with the HEX you will be starting from scratch, including any journey from Paddington to your accommodation.

The actual effect will vary depending on your plans but with many visitors arriving in the morning the difference could end up being significant.

The difference is not especially significant- the Zone 1 /2 fare cap is £8.90 per day so £10 + £8.90= £18.90 versus £16.30 Elizabeth Line/tube fare cap- a £2.60 difference.

If you have any National Railcard due to other journeys during the trip then Heathrow Express + the cap actually works out cheaper- because the £10 Advance Fare on HEx becomes £6.65.

If that railcard is a Senior or Disabled one and you register it and use an Oyster card then the £8.90 Zone 1/2 daily fare cap becomes £5.90, so the £10 cost of an Oyster pays for itself on Day 4.

If you have mobility limitations or physical impairment, it is helpful to know the following: if you take either the Elizabeth or Piccadilly lines you may end up standing for a good portion of your journey, as we did this summer. Additionally, if you are unable to climb or descend a flight of stairs with your luggage you ought to confirm whether the tube stations where you'll need to do transfers are stair-free -- otherwise, again, you may end up needing to climb a flight of stairs with your luggage when you transfer.
If you prefer to avoid the possibility of any of these challenges, you can take the Heathrow Express to Paddington and then take a taxi to your hotel.

If you start at Heathrow you won't be standing up whether you take the Elizabeth or the Piccadilly lines - they both start at the airport so there will be plenty of seats. Coming back from central London to the airport seats will be at more of a premium. Generally though, seats will be available on the Elizabeth Line from Paddington onwards if not before, unless you travel in the evening peak.

If you absolutely must avoid stairs, the best route using only stepfree stations is Elizabeth Line to Bond Street, then Jubilee Line to Green Park and bus 9 or 23 to Charing Cross. On the bus you'll pass through Piccadilly Circus and Trafalgar Square.