What is the cheapest way for a family of 5 to get from Hong Kong Airport to the Cosmopolitan Hotel?

Bus is the cheapest. But there is no direct bus that runs between these two places. You need to transfer.
Upon landing, take bus no.E21 at Airport (Ground Transportation Centre), get off at Sham Shui Po Station, Cheung Sha Wan Road. Then transfer to bus no. 112 at Pei Ho Street, Cheung Sha Wan Road, and go to South Pacific Hotel, Morrison Hill Road. The duration is about 125 mins. And the ticket fare is 23.3 HKD per person.
After arriving, walk southwest around 300 yards to find your hotel.