You should take Changsha or Zhuzhou by train. Changsha and Zhuzhou are both very close to Xiangtan, so it takes about 1 hour to change buses. Maybe Zhuzhou will be closer and the ticket will be a few dollars cheaper.
If you fly, you'd better choose to arrive during the day. Because the bus from Changsha to Xiangtan doesn't leave until 9: 30 at the latest. Besides, Huanghua Airport is far from the railway station (Changsha-Zhuzhou-Xiangtan bus station is near the railway station), and taking a taxi is quite expensive.
When I say half an hour upstairs, I mean some bird cars, that is, some private passenger black cars. Because I don't take the expressway, I take half a soup to Xiangtan Hedong. So it usually takes only half an hour. Personally, I don't recommend it, because it's not safe, driving too fast and not obeying traffic rules, especially at night. However, if you choose this one, you can ask me for the driver's phone number.