please advice how best I can travel from Mumbai to Changsha. wants to explore flights and train mode

Well, you can fly to Beijing directly first. Take PEK shuttle bus line 7 to local West Railway Station, where there are high speed trains to your destination. The train journey is around 7h. To save time, you cans surely choose to catch the flight to the city instead.

how about the following plan
A. Distance from International Airport to CS and the Nearest International Airport

1. Shenzhen Baoan International Airport (SZX)
2. Guangzhan Baiyun International Airport (CAN)

B. Mumbai to the nearest Airport ticket rate
INR 32500 for both
Travel time from M to S = 12 hours / Return 29 hours
Travel Time from M to G = 12.30 hours / Return 21 hours

1.1 S International Airport to S North railway station
– by bus, taxi, Train = 50 minutes (36 KM)
Bus every 30 minutes - Charges=RMB 25
Taxi – 100 RMB
Train – 7 RMB

1.2 S North Railway station to CS South
High speed train
Good frequency
Duration 3.5 hours
_______ KM
Charges RMB 66 to 400 RMB
Reaching after 8.00 pm before 11.00 PM

2.1 G Airport to G South Railway station
Distance- 58 KM
Mode: Metro Train (not preferred during peak hours), Taxi
Train duration _________
Taxi : charges RMB 190 to 200

2.2 G South Railway station to CS South Railway Station
707 KM
High Speed Train
Charges RMB 350
Train duration 2.3 hrs to 3 hrs
Timing 6.30 am to21 pm