Situation: Me and my co-traveler will arrive at Beijing Capital Airport on 11:55 on May 2, 2016 and plan to take a taxi to Beijing South Railway Station and a high speed train to Tianjin. (This seems to be the best way for us to travel to Tianjin, since all available flight connections to Tianjin include an extra layover and at least 5 hours extra travel time compared to the Beijing connection.) Having checked earlier SE questions on the topic and other online resources, I get the impression that it is advisable to just buy tickets at the station. Since we don't know how much time customs, baggage claim and the taxi trip will take, this option may be preferable. On the other hand it seems to be relatively easy to book tickets online which may be preferable if the trains tend to get full.
Questions: Is it common for the high-spped trains from Beijing to Tianjin to get fully-booked around 13:00-15:00 on weekdays? Could several consecutive trains be full? Can you (always) buy a standing ticket on a full train? Also, how difficult will it be for us to buy the tickets and find our way at the Beijing South Railway Station? (We don't speak Chinese or read Chinese characters. We have been to China before, but have mostly been accompanied by Chinese friends.)