Just wanted to echo what some of the others have stated. To do a good job in security you really need to understand how operating systems and protocols work and work together.
Someone I met before took a cut in pay to work first level helpdesk and studied his butt off the entire time. That job taught him what troubles to expect and what he was learning (mainly Cisco classes) brought in the networking knowledge that he needed. After three years he was making double what he had before, had a couple of certs under his belt, and working on a couple of others.
And yes, learn some programming. I have not done much in... well, a long time and if I do not change that it will hold me back. Once you start getting a solid understanding of networking and the basics of security things will make more sense as you move deeper into the security realm.
While having a goal to work toward to is great, be sure to keep your mind open to what is going on around you. I originally wanted to do PenTesting and some of the really neat stuff that others talk about but I have ended up making the biggest impact on the administrative side. While not as "glamorous" it is necessary and gives security a very public face within an agency/business.
Another book to add to the list (IMHO):
Counter Hack Reloaded by Skoudis and Liston
Read it after going through the Security + material.
Good luck and let us know what ends up working for you.
