I will be in London for 9 days in the fall and I have been looking into this myself. Days 1 and 9 will be half days transiting to and from LHR and I will use my Oyster card on those days. But it appears that it will be much cheaper for us to get the zone 1&2 7 day travelcard for the middle days. It appears that good deals can be had on the Visit Britain web site to order it a month or so before we depart and have it shipped to us.

We will likely use the Heathrow Connect to get to and from LHR.

It sounds like we would then have the old-fashioned paper cards. It also appears that doing it this way will be a bit cheaper than loading the travelcard onto our Oysters.

I used to just use Oyster for every day (normally we're there 7-8 days when we go) then learned that we paid too much using Oyster only. So this seems like the way to go.

If anyone has other suggestions, please share!