HKIA to Lo Wu

Hi.
We were planning to go to Shenzhen from HKIA. We were told to get on board an 'A' (A21) route airport shuttle airbus to Hung Hom (East Rail Line) MTR station. Then take the East Rail line to Lo Wu. Is this correct, as it seems very simple.
Would you be able to let me know if Hung Hom station has easy access to the train from the drop off location, as each of us will have our checked in suitcase and a carry on bag. Can you also let me know how long it would take from the HKIA / Hung Hom / Lo Wu?
Thanks very much for your help!!!