To those discussing train option.
If you plan on going from London Paddington.
You have the Heathrow Connect and Heathrow Express.
Heathrow Connect is cheaper, but on a Sunday is normally only an hourly service taking about 25mins leaving 12 minutes past the hour. £6.90 single or £11.90 day return.
Heathrow Express runs at a frequency of every 15minutes at 10/25/40/55 past the hour. Takes about 15mins. £15.50 single £29.00 return, or ask for a meet and greet ticket but I'm not 100% on this tickets restriction.
If you are travelling from further afield by train, you just need to buy a ticket to "Heathrow Rail"
A terminal does not need to be specified, from personal experience I would recommend you go to Heathrow Central (Terminals 1,2, and 3) and there is a bus from the Central Bus Station which when I last used it was free, and takes you near the hotels on the Bath Road.
If anyone has any train issues, get in touch with me and I will try and help you.