How long it will take from Tianjin airport to Tianjin Railway Station, from Beijing South railway station to hotel near Forbiden city?

my wife and i will be visiting Beijing from 29th Dec 2010, our flight will be landing in Tianjin airport at ard 2:30pm, what would be the estimated time for travelling if we were to take a cab from the airport, then transfer to the bullet train and cab from Beijing to the hotel (very near forbidden city)? would it be advisable to purchase the train ticket in advance?