We will be in London for 5 days. Arriving Heathrow,depart Luton. What passes should we use?

We are staying in Golders Green and would like to tour in central London for 4 days, including the first day when we will go right from the airport to see some sights (on the last day we'll likely go just to Hampstead, which is close to GG). Can you please help advise what London tube/rail passes will help us economize? In addition, we are quite confused as to the least expensive and quickest ways to get from/to these airports. Certainly we can take buses, but this seems like another layer of information I don't feel adequate to take in ... many thanks.