train station closest to Heathrow

Your destination will determine which train station in London you will use. Where do you wish to go after flying into Heathrow?

Paddington.

I think its terminal 3 (Air Canada) fying to Toronto.

Thanks for the rail tips, all!

I thought you were going on by train to somewhere in the UK after flying into Heathrow. It now sounds like you were asking how to get to Heathrow from London. If that's the case, rail reservation sites won't help you because they don't show timetables for the London Underground. The cheapest way to get from London to Heathrow is to take the Tube (subway). The Piccadilly Line goes to Terminals 1-3, 4, and 5.

I may be traveling by rail from Holyhead/Wales to London after a week in Dublin - see previous question I posted re Dublin to London. (my other option would be to skip that one day in Wales and fly direct from Dublin to catch my flight out of London Heathrow...)
The train routes from Holyhead show many options, just not Heathrow. Looks like Paddington is the answer.
Thanks to all posters for your helpful replies :)

Trains from Holyhead to London arrive at Euston, not Paddington. Take the Tube to Heathrow: Victoria Line from Euston to Green Park and the Piccadilly Line from there to Heathrow. The ride will take about an hour and the fare is 4.50 GBP. For a Tube map go to this page on the Transport for London site and click on "Standard Tube map (PDF 0.26 MB)".

Susan, Heathrow is the terminus for one branch of the Underground's Piccadilly Line. From Paddington Station you can catch two trains to Heathrow: the Heathrow Express and the Heathrow Connect. The latter is slower, makes a few stops en route and costs less. Google them directly to find details about fares and schedules.

The Piccadilly line obviously has many stops in London. It's the cheapest, but the slowest, way to get to Heathrow. If you are traveling with only minimal luggage it should serve your needs. Hauling more than minimal luggage on and off the Tube, while common, can be a hassle. Google "Transport for London" for more than you ever wanted to know about the Piccadilly Line and the rest of the Tube.

If you are traveling late at night, pay attention to the closing hours for the Tube and the trains.

Thank you all for this great travel advice! London train and tubes have always confused me...
I will go to Cardiff, Wales after the week in Dublin. From Cardiff i will either fly or take a hi-speed train to London and stay overnight in a cheap hotel close to Heathrow on the bus/shuttle line so I can catch my early flight departing terminal 3 very early.
Sounds like a better idea than taking a night train to London with late night tube to Heathrow and sleeping in the airport (my original plan :)

The trains from Cardiff arrive at Paddington. You could then take the Express or the Tube to Heathrow and stay at an airport hotel (such as the Yotel).

There is also the less expensive Heathrow Connect train from Heathrow to Paddington.

From Cardiff, you can take a train to Reading and then switch to a bus to Heathrow. No need to go into London.

Your hotels choices, as previously stated, range everywhere from inexpensive hotels on the shuttle bus line to the Yotel in Terminal 4 where you pay by the hour.

Susan, my wife and I tried the Yotel in Terminal 4. About 70 pounds for the night although they charge by the hour. It was small but clean and extremely convenient in being close to our flight home. Very modern with free internet. There are also a couple of nice restaurants on the check-in floor above. You are also very close to the trains below to get you to the different terminals.

My wife and I still chuckle about our Yotel experience. It was small but no smaller than some places that we have stayed in Italy and it really worked to be near the plane.