Hi Wayne,
Travelcard/Oyster card
You can pre-order your travelcard and have it delivered to you in Canada, it is a smart card called an Oyster card that you swipe on the barriers at the tube stations and you can get it from here.
http://visitorshop.tfl.gov.uk/
You may only need zones 1&2(£25.80) if you stay pretty central and don't use the tube from Heathrow.
Travelcard prices are here
http://www.tfl.gov.uk/tickets/faresa...kets/4805.aspx
Check the map here to see what zones you'll need.
http://www.tfl.gov.uk/assets/downloa...t-tube-map.pdf
Getting from Heathrow to your VERY NICE hotel in the "West End" (Down Town)
The least stressful way would be to get a taxi direct from Heathrow; costs somewhere between £40-£75 to get to the West End and could take over an hour dependant the time you land.
http://www.tfl.gov.uk/gettingaround/...axis/1140.aspx
The fastest, reasonably priced (£18)
(and in my view the best) way to do it would be the Heathrow Express rail service to Paddington 15mins from Terminals 1-4 or 21 from T5, then a Taxi from Paddington station to your Hotel (£10, 10mins)
http://www.heathrowexpress.com/Home
As the nearest tube station to your hotel is on the Piccadilly line (Hyde Park Corner) you can go direct from Heathrow on the Tube although you'll need a zones 1-6 travelcard (£47.60) to cover the whole journey.
I assume your coming on a red eye so will run in to the morning rush hour when you arrive. The Tube would be a bit of a squash at that time especially with your luggage. Plus you'll have to manage your luggage up and down the escalators
Anyway dependant on how tired you are, much money you want to spend and how quickly you want to get to your hotel these are your best options.
If you got the Heathrow Express to Paddington, you could get the tube from Paddington to Hyde Park Corner, but that is two short tube journeys (Bakerloo & Piccadilly lines) and then you have the transfer between the two lines and getting down and up from street level and then the short walk to your hotel which would in my view be pointless, you might as well get the tube from Heathrow direct.
Travelling on the Thames
If you want to visit Kew Gardens or Hampton Court then you could get the River Bus from Westminster Pier, the service to Kew & Hampton Court is very limited so you might end up getting a train (Hampton)/tube (Kew) back. Richmond is a nice town to stop in too.
River Bus service details here
http://www.tfl.gov.uk/assets/downloa...tt-leisure.pdf
You get a very good discount with an Oyster Card here
http://www.tfl.gov.uk/tickets/oysteronline/13411.aspx
The other river activity you must do, is to go on the "Duck tour", it's an amphibious bus used for the D-day landings in 1944 that gives a good (but short) road & river tour around the Westminster area
http://www.londonducktours.co.uk/
You join the Tour right next to the London Eye so you can combine that with the tour which is right next to the London Aquarium & I'm not sure if they still have the Salvador Dali exhibition on near there as well.
A word on mini-cabs
These are basically pre-ordered chauffeurs in normal cars, they are about 50%-75% of the cost of Black Cabs (Taxis) are licensed and cannot pick up passing trade. The tube stops at midnight generally so if your out and about late at night then you might want to pre-order a "mini-cab" from your Hotel before you go out; if you know where you'll be and what time you want to be picked up. Alternatively you can call from where you are or ask the staff to get you a mini-cab. The later you leave your booking the longer you'll wait and more it will cost. They are very much preferable to using the late night Bus services which are an experience all on their own.
See here for more details and some good advice.
http://www.tfl.gov.uk/tfl/gettingaro...e/default.aspx