From Zhengzhou to Tianmen Mountain Hunan Province

We want to go from Zhengzhou to Tianmen Mountain by train. I see it takes 2 hours 45 minutes to Tianmen South station. How far is it from there to the mountain and what is the best mode of travel please? We will spend 3 or 4 days in the area in order to see the many areas of the park and mountain. Where do you recommend we stay? Is there a mountain temple to stay at one night? And is 3 days a good amount of time? We love nature. Many thanks.