So in which order should I fill my choices. I mean should I give upper NIT's preference over lower IIT's and should I go for lower brances even in IIT?

There are no upper or lower branches, every branches has its own importance. Which branch you are interested give it as your first preference and then other branches. First give IITs then NITs. Many candidates go with Mechanical, CSE but the seat are few so it is not possible to get seat easily on this branch. So give other branches preference so that you will be able to into IIT but also do some research about the branch you want to go for as it is interesting field for you to work in the future or not. You should have interest that branch.

Thank you so much for your assistance. ️