Should I go for the Integrated MTech course in IIEST or rather do the BTech in Jadavpur University or some NIT (say, DGP or Calicut) and then try and get a better college for my MTech?

I have a few friends from IIEST. According to them, choosing IIEST can be good. For departments like Mechanical, Electrical, Civil, Mining, the faculty base of IIEST is great. The civil engineering department at IIEST is one of the oldest in the country. Also, as per the new norm, you don’t have to complete a dual degree. 

You can have an exit option after completing your 4-Year B.Tech. Which is definitely a good option. However, if you want to choose CS/IT, for placements, top or average NIT/JU will offer better placement opportunities. 

So, consider all your options and choose according to your convenience.