Which NIT or IIIT is good for me as per my OBC category rank of 9788? Can you also let me know the branch?

I don't know about IIIT, so I won't talk about them. As your home state is Haryana, you can easily get NIT-Kurukshetra's ECE and EEE branches. Of both the branches, I think ECE is better. But it purely depends on your interest.