I will be traveling to Oxford, UK this summer. My flight lands at Heathrow around 12:30pm on a Sunday; it is on British Airways so I believe it will arrive at Terminal 5. Based on this map and other resources, it appears that one can take a train from Heathrow to Hayes & Harlington station, and then change to a train bound for Oxford, thus avoiding the need to travel into central London and backtrack.
However, on closer inspection, it looks like the trains from Terminal 5 stop only at Terminals 1,2,3 and then run express to Paddington Station, without stopping at Hays & Harlington (I think this is the so-called Heathrow Express). So I would need to first transfer to one of the other terminals' rail stations and catch a train from there.
Is it reasonably convenient to transfer between terminals like this? Some sources seem to suggest that the best way is to take the Underground to the other terminal. How easy is it to get from the Underground station to the rail station at the other terminals?
Would it be better to transfer to Terminals 1,2,3 or to Terminal 4?
Are there other good options that I am missing?
I will probably not have an excessive amount of luggage.