Each branches are good it depends on your interest & capability.  Some of the core branches:

CSE : It is not only development & coding  but also testing and life-time support, which needs CSE engineers in drove. The major chunk of jobs offered in India, every year, are for CS engineers.
The expected salary for freshers is from around Rs. 3 Lakh PA to Rs. 5 Lakh PA for jobs. The package also depends on the institute & the organization.

ECE: An electronic engineer can find a job in Consumer electronics manufacturing organization , Telecommunication & IT industries, Internet technologies, Power Electronics, and other industries like steel, petroleum and chemical industry. The salary range for EC freshers  from around Rs. 2.5 to Rs. 3.5 Lakh PA. It also depends on the institute & the organization.

EEE: Electrical & Electronics engineers can work in wide range of fields such as power generation, electronics, computers & control systems, telecommunication and Bio-Medical. The starting salaries for electrical engineer freshers range around from Rs. 3 Lakh PA to Rs. 4 Lakh PA. It also depends on the institute & the organization.

ME: India always had robust heavy-manufacturing industries like steel, metal, forging, automobile and mining. All these industries require steady inflow of fresh Mechanical engineering graduates. The starting salaries for mechanical engineers range from around Rs. 2 Lakh to Rs. 4.5 Lakh. It also depends on the institute & the organization.

Civil Engineering: Civil Engineers are usually required in every field some of them: Government Departments, Local Authorities, Civil Engineering Contractor, Civil Engineering Consultants. The starting salaries for Civil engineers range from around Rs. 3 Lakh to Rs. 4 Lakh.

Colleges:

Top Engineering colleges

Good Luck!

Engineering is a career to build the nation. The cse it branches deal with coding and software related subjects.ece eee has electronics as majority with connections and communication networks. Mechanical has machine building subject. Civil has construction based subjects with measuring. For high salary option cse it ece are better options