best way to go to changsha from meizhou

For Meizhou, do you mean the one in Guangdong Province?
If so, you can take the direct bus to reach Guangzhou Tianhe Bus Station or Yuexiu Bus Station and then take trains from Guangzhou to reach your destination city.
From Meizhou to Guangzhou, the bus will take you about 5 hours and from Guangzhou to the city you want to go, it will take you about three hours by taking bullet trains.