Want to go to linyi from shanghai by fast train and then to Hunan by car.

There is no bullet train but one normal express train to Linyi, leaving at 13:25 and the travel time is about 17 hours. If you don't mind, it's suggested to take a bus instead. In the General Long-distance Bus Station, direct buses are scheduled from 06:40 to 20:50 each day and it takes about 8 hours.

Hunan refers to a large province, do you refer to the capital of the province, Changsha city?
It is far between, and it would cost a lot if hirng a car. You can take a train from Linyi North Station to Changsha instead.