how to get to Zhuzhou better from Beijing or from Shanghai ?

In my opinion, it is better to travel from Beijing. Though only three trains are scheduled from Beijing to theis city, one of them is bullet train and you can reach in around 6h and 50min. If traveling from Shanghai, no bullet train is available and the travel duration shall be 9-11.5h.

you can take a plane from Beijing or Shanghai to Changsha,the Capital city of hunan province,and change a bus to the destination city,it will take you about 40 minutes.