Getting to EATON Hotel from Hong Kong Airport

Am I correct in thinking we get the Airport Express to Kowloon Station and then a free shuttle to the hotel?
Do we buy an Airport Express Round trip ticket and an Oyster card or will the Oyster card do it all?
We will be wanting to also get about on the MTR.
At this stage we will only be in HK 2 nights but on our return from Europe we will be staying four days.