NIT

Select the branch of engineering depending on your area of interest.
Here are some of the streams, out of which you may select based on your interest:
1. Mechanical engineering
2. Civil engineering
3. Chemical engineering
4. Electrical engineering
5. Biotechnology
But, be cautious while choosing the institute as it play an important role in making your career. Always go for the one that along with good education provides practical exposure. Here are some of premier institute which you may select:
1. IIT
2. BITS
3. Lovely Professional University
These institutes along with good education are also providing an excellent platform to their students to boost their skills making their students easily employable. I have heard a lot about Lovely Professional University-its ranking, recognition, tie-ups, infrastructure, placements etc. Hope it helps.

There are many good engineering college besides IIT's and NIT's, I have tried to list some of them. Caution: This ranking is done on CSE and other Core Branches. Please keep branch in mind before deciding. - BITS Pilani (Pilani + Goa + Hyderabad) +IIIT Hyderabad (mecca of coders)
- BIT Mesra, Ranchi (old brand value)
- DAIICT Gandhinagar (+1 coding culture)
- RVCE + PESU Bengaluru (good coding culture because of Bengaluru, but bad perception because of management quota, COMEDK)
-MIT Manipal & VIT Vellore (Well Established brand, but huge batch size and fees, management quota in VIT )
-Thapar, Patiala&PSG, Coimbatore (Good brand but huge state quota)
- JIIT Noida, LMNIIT Jaipur & NIRMA Ahmedabad (decent one for CSE), PDPU Gandhinagar (Petroleum)
-NSIT Delhi
-Delhi Technical University
-IIIT DELHI (Course structure is awesome +huge exposure + placements are very good)
-HBTU (mainly known for its core Branches)
Comments and discussions are welcome. If you find this answer helpful then please upvote.