Binaya, if you have a GC then you will get some level of security clearance. I recommend getting some popular certification. I would start with CCNA even though everyone hates cisco.

Then after move on to something enterprise level product. routing switching is something I don't like at all so I don't suggest that at all but CCNA will give you all the fundamentals you will need.
--- If you want to get into real security security then start on getting you CEH cert ...its actually a fun cert. Then after you can move on to many other stuff such as Malware analysis, Firewall engineer , IPS , IDS , Proxy etc. If you do get into Firewalls , start with a simple linux firewall and move up to a enterprise grade firewall such as a SRX , ASA ,NSX, PAN or checkpoint. You will need linux everywhere so the basics of bash is extremely important everywhere.

-- Know how to run a packet capture and how to analyze one in wire shark. Remember packet traverses through all OSI layers. You have to know TCP handshakes and how it behaves. Movin up learn how https and most importantly https works (ciphers / ssl certificates / authentication ) etc.

Lastly i would say that security nowadays is essentially an infrastructure, automation is inevitable so secOPS concepts such as docker / ansible / puppet/ openstack  / AWS  etc are the future.