This is my view, read just for fun.
First the learning part —
If you are very specific to Data Analytics field, you just need to be good in these things —
1. Standard Algorithms used in Data analytics and how you implement them.
2. How to model problem in such a way an optimal result or information can be drawn from it
3. Good knowledge of programming (functional and parallel would add extra points) and visualization
4. Domain knowledge of problem you are tackling!
Later, the money part —
Package of company would directly proportional to how company sees it. If you can solve and model problem for your company I hardly see any issue. How you define higher package? Does your company takes few things into consideration before raising or promoting pay raises?
The Good institute's part —
IIT/IISc/NIT would definitely give you chances to sharpen your skills be it in any domain — its all upto you do you wish to study or want to continue working on real-world project and sharping skills during that period!
Later my personal part —
Learn and solve problems, solve it in very optimal and efficient manner — from approach to programming. Work for some company until you get good knowledge, Switch or ask for raise! Better start your own!
Anyway, let me know your thoughts. And hope you shine in your Data Science career, best wishes!