You should choose the branch according to your interest and passion. If we compare the branches then CSE is the most popular branch followed by ECE, Mechanical, Civil, Electrical and IT.

It's depends on the college. You should always choose the college which provides good placements.

Below is the list of top private college you can check

Amrita School of Engineering, Coimbatore

Birla Institute of Technology and Science, Pilani

BMS College of Engineering, Bangalore

VIT University, Vellore

Manipal Institute of Technology, Manipal

PSG College of Technology, Coimbatore

Ramaiah Institute of Technology, Bangalore

RV College of Engineering, Bangalore

SASTRA University, Thanjavur

SRM University, Chennai

To check the complete list you can refer below link

Top Engineering Private Colleges

Good Luck!!