It isn’t a bad career. However The two classes you listed are not enough really. In addition, I’d take computer security classes and consider Novel, Microsoft and Cisco certification as well. Ideally, you should have a college degree in computer security.

well those will get your foot in the door to maybe a PC technician, then maybe helpdesk support, then maybe to network administrator for a small network which will include LAN & internet security then maybe a larger company more specifically with network security. Its going to take experience no matter what

you may want to get your MCSA or MCSE certification through Microsoft. Then get at least a BS in Information Technology. Make sure you take a Cisco Networking class!