There is subway from the airport, but you have to transfer for two times to get to Tiananmen, so not suggested if you have luggages. From the airport, you could take the airport shuttle bus Line2 and then get off at the terminal of Xidan which is just to the west of the Forbidden City.

Hiring a taxi to the port from Beijing to the port directly? The fare is no less than 400RMB. On the other hand, you could take the express train from Beijing South Railway Station to Tianjin Tanggu Railway Station, just takes one hour and 77RMB per person. Get off the train, you could take a cab to the port, just cost around 10RMB.

Thanks for the response. I'm particularly concerned about access to the public transportation (bus and train options) during this National Holiday period. Will seats be available? Our arrival in Beijing on Oct 3rd around noon would put us on the downtown bus in early afternoon. On Oct 5th we would be going from downtown to the Tangin Xingang port, again in the early afternoon. Will crowds make travel with baggage too difficult to manage on those routes and times?

You are right, during the national holiday, the train ticket may be needed urgently. But, if you could do reservation in advance on Oct 3, seems you still could get a ticket with seat. Baggage will not be problems, except they are huge~ Just for your reference!