To make your life in London easier best to refer to the London Underground as the tube.
Trains as in "then catch a Train from Paddington Station to the Hotel." simply confuses.
Secondly the 2 for 1 offer does not include the tube. Thus you cannot buy it an an Underground Station. You must buy it at a Train station: Paddington, Victoria, Kings Cross, St Pancras.
The closest TRAIN station to your hotel is Victoria.
There are a number of different ways to get into London from Heathrow, from costly and quickest to slowest and cheapest.
Heathrow Express and the bit slower Heathrow Connect are the most expensive but the quickest. Express is a 15 minute ride. Both arrive at Paddington Station where you will find access to the Tube.
The cheapest and slowest route into London is on the Piccadilly tube line.
You can also take at National Express bus, arrange for a car hire or take a cab.
STOP using Google maps to find your best route option. Use this website instead. https://tfl.gov.uk
You've chosen a hotel that is not in the London center so it will not be a direct line from Heathrow anyway you look at it.
So look at the London Tube Map https://tfl.gov.uk/tfl/syndication/widgets/tubemap/default-search.html
Ask you hotel what's the easiest route from Heathrow but if you wish to use the Underground as your means of transport to your hotel you will need to take the District Line (the green line) to Fulham Broadway Underground Station and then walk 12 minutes to the hotel. That way you can discover where the closest Starbucks, bank ATM and market are located.
Or take the District Line to West Brompton and get on the Overground toward Clapham Junction and take it to Imperial Wharf and then walk to the hotel.
What you will first need is an Oyster Card for the Underground and Overground and busses. GET THAT at Paddington.
There are machines. Easy Peasy.