Pick up any of the Engineering discipline like Electrical, Communication etc and add Networking courses to that. Then work on getting your CCNA certification on the side, this will give you the best hardware and Networking combination.
Electrical and/or Computer Engineering would be a great place to start. If networking is your passion, that's great! (It's mine too). You'll be able to layer-on Networking. There are many parts to networking where a core in the underlying engineering fundamentals will help you. Besides electrical, radio and optical networking may have specific tracks depending on your interest.
As for a career, you'll find that networking companies hire more electrical engineers (and low-level software engineers) than they do network engineers. In other words: Electrical engineers build networking products. Network engineers use networking products.
Example companies: Broadcom, Mellanox, Intel, Huawei, Cisco, Nokia (Alcatel Lucent), Qualcomm, Apple, Samsung
If you think you'd rather be a network engineer (especially in an Internet-facing infrastructure), checkout some of the conversations at http://mailman.nanog.org/pipermail/nanog/ or the presentations from NANOG's meetings http://nanog.org/meetings/archive (all open and free)
If you are really interested in Networking than Engineering in ComputerScience/IT will best suit you, if you choose some other stream like Electronics/Electrical/Civil/Automobile then you will lose 2 years of your experience when you apply for immigration to countries like Australia.
The reason they give is your major degree does not matches with your current experience irrespective of B.Tech/B.E.
Its not about going abroad but choosing relevant path which will benefit eventually and if you choose networking then start learning scripting languages, when you are through with your studies you will stand a brighter one.
All the best!
Great to know about your interest in Computer Networking. The first step you should consider is getting a degree in Computer Science or Electronics and Communication.
Computer Networks is wide domain and you can place yourself in many suitable areas. One of them is IP Networking. This field has evolved a lot over the past 15 years and there's plenty to learn. There are new technologies emerging everyday and the scope for further research is endless. You get to understand the inner workings of Internet, how data gets sent across, how security is implemented and much more. The career as a Network Engineer is very promising.
Another emerging field is the Internet of Things. The aim is to connect simple devices and sensors to internet and process the data they produce to suit our needs. An example can be connecting a temperature sensor and Fan inside a room to a controller via internet. When the temperature crosses a certain threshold, the Fan should turn on automatically. This field is a good mixture of hardware and networking and is promising as well.
I'm old fashioned...but think you should consider Math.
Best said by Keith Devlin ..."If you want to prepare people to design, build, and reason about formal abstractions, including computer software, the best approach surely is to look for the most challenging mental exercises that force the brain to master abstract entities — entities that are purely abstract, and which cause the brain the maximum difficulty to handle. And where do you find this excellent mental training ground? In mathematics"