Trains--transfer time needed ?

I am going to pre-book some trains for our trip in early September. We will arrive in Taiyuan 11am from Bejing by train. We need to catch the next available train to Pingyao. the schedule says the next one is at 1125am. Is this enough time to transfer to this train at the station without rushing? Or should we wait for the next one (1 hour later). Also, we are arriving at Changsha bus station around 3pm a few days later. We need to get to the Changsha South Train Station to catch a G-Train. What time is a good train to book, 4pm? 5pm? We don't want to rush but we don't want to wait around too long.