Oyster Card or Travel Card

Larry,
An Oyster Card is valid on the Piccadilly line from Heathrow to central London, but this is the slow route (40-50 minutes).
The alternative is the Heathrow Express (15 minutes) on which the Oyster Card is not valid. It is not a "suplement", you pay full fare whether you have an Oyster Card or not. The Heathrow Express goes to Paddington station, so unless your hotel is near the station you still need to use the tube (and use your Oyster Card) to get to your final destination. Depending on where this is, it may use up some of the time advantage of the Heathrow Express.

No need to buy your Oyster card before you leave home, you can buy it at Heathrow tube station, or at Paddington,
Oyster card is valid anywhere in London (except the Heathrow Express), not just zones 1 and 2.

Do you have a contactless debit or credit card which has is free to use in the UK?

If so you don't need an Oyster or Travel Card.

If you tap in and out with the same contactless the same capping, daily and weekly, applies, no reloading or topping up, and when you register the card you can view your entire usage history on line.

On the other hand if your bank doesn't play or you don't have a contactless (or Apple Pay, or smartwatch, etc., or Google Pay, etc.,) you could do the Zone 1 and 2 weekly Travelcard and have a small Oyster or single tickets for the airport. For a full week of use, I'd say weekly Travelcard or contactless.

You can't use Travelcards or Oyster Cards on the Heathrow Connect or Heathrow Express which require tickets; you could use an Oyster Card with some Pay As You Go (PAYG) on the Piccadilly tube Line into town, and the Piccadilly Line goes all sorts of interesting places.

Nigel, tap-and-pay credit cards are still not common in the US. They are widespread in Canada, but with a major drawback: various fees for transactions in foreign countries. That could mean $2-$5 extra for each Tube tap. Quite expensive for such convenience; I will be purchasing a real Oyster card.

I use my Oyster whenever visiting London and have been very happy with it. I always ride the Tube from Heathrow into London and catch a taxi to my hotel if it is not conveniently near a tube station (only about 5 pounds for the tube ride! Much more affordable than the Express and it is a great hour of people watching). I am usually there for only a few days, so the 7 day travel card does not provide any benefit to me. Also, I bought one of the "visitor" cards you get from a travel agent or elsewhere outside the London area. It has limitations. I would suggest you purchase your Oyster at the Heathrow tube station. You then get a "real" Oyster that allows many options for storing combinations of travel cards and cash on the single card. And the remaining cash total including the 5 pound deposit is fully refundable when you depart.

You can purchase a 7 Day Travel card for the zones you will be going through and have that loaded onto the Oyster. The good thing about this is that if you have a 7 Day Travel Card for only zones 1 -2 (best option cost wise) loaded and happen to stray outside that zone, the Oyster system takes care of that and you pay the supplement automatically from the funds on the card. Much nicer than getting to the tube exit and your travel card won't let you out because that station is outside the zone you paid for. And on days you want to stray outside the central zones, you don't need to worry about getting a day card or other option because the Oyster will never charge you more that day than you would have paid for the equivalent 1 day Travel Card.

I appreciate your feedback very much, but, sorry to say, to a foreigner from Florida it seems confusing. A larger problem is, I'm bringing with me four high school classmates (class of 1958-75 years old). I'm in charge of transportation so I have to give them advice and explain it to them. It's a daunting task. I think I'll go with the Oyster Card and we'll take a taxi to and from Heathrow. We can afford it, our wives are staying at home. I'm also in charge of pub crawls.

Larry,
Transport in London is easy. 5 people = 5 Oyster Cards. It is simple, with an Oyster Card you can go anywhere in London, by tube, bus or train; with one exception, the Heathrow Express.
Of the 3 methods of getting from Heathrow to Central London (Heathrow Express, Piccadilly Line (tube) and taxi), taxi is probably the slowest during the day. It is also the most expensive if you are on your own, but probably economical for 5 people.
According to: http://www.taxifarefinder.com/main.php?city=London&from=Heathrow+Airport%2C+Longford%2C+United+Kingdom&to=Covent+Garden&fromCoord=51.4700223,-0.4542954999999438
A taxi (slowest) would cost about £70, that is £14 per person.
Tube = £5 (Mon - Fri, 06:30 - 09:30) and £3 (all other times). That is with an Oyster card (see here)
Heathrow Express (fastest) = £22 per person, but you still need a tube or taxi for the "last mile".

I got off the plane at LHR and asked where the Tube Station was. I found it, bought an oyster card and made it to the Docklands all by myself! It was so easy. You can do it!

Your best bet is to get an Oyster card and ask the teller to put a 7-day Travel Card on it that covers Zones 1 and 2. This is what I did last time I was in London (2014), and it made getting around incredibly easy. There is a Tube station right at Heathrow, and you can get your Oyster there -- I believe you put down a £5 deposit but you get it back if you return the card to a teller before you leave. You also get a nice little sleeve to keep your Oyster card in, and intentionally or not, I got to keep it and now use it for my ORCA card here in Seattle :)

I believe you put down a £5 deposit but you get it back if you return the card to a teller before you leave.

I didn't have time to return my card Oyster card before we left London. When I got home to the US, I simply mailed the Oyster Card back to London and I received the deposit plus any leftover monies that remained on the card. Just go to the official website for return information. I sent it back, but I really didn't think I would receive a check - but I did. :D

If you can’t visit an underground station before you leave, send your Oyster card and photocopied proof of name and address to TfL:

Oyster Refunds
4th Floor
14 Pier Walk
North Greenwich
London
SE10 0ES

Refunds by post will be sent by cheque (£) or by bank transfer to your bank accounts (UK addresses only).

If you have any questions, contact TfL Customer Services on 0343 222 1234 (open daily 8am–8pm).

Worth mentioning I guess that TfL does not charge each journey to a contactless form of payment individually, but once a day.

It only took a few weeks to receive the refund - I was really surprised how quickly I received it. I deposited the check (it was in Euros) into my Bank of America account. The bank simply converted the Euros and deposited the converted amount as dollars to my account. Easy Peasy 😀

Edit: Check was received in Pounds not Euros.

Pilgrim, it is surprising that they sent the funds in Euro, as Euro is not a currency recognised in the UK.

So that was a lot of conversion - Pounds to Euros to Dollars.

Did you have anything left after all that?

Pilgrim, it is surprising that they sent the funds in Euro, as Euro is
not a currency recognised in the UK. So that was a lot of conversion -
Pounds to Euros to Dollars. Did you have anything left after all that?

Oops, Nigel, you're right. It was Pounds. I'm in Italy mode right now so I've been thinking in Euros lately. :)