I'm the manager of application security and research at a mid-level software vendor with over 400 developers and testers and I want to recommend you ignore all of the more generic advice currently in this thread. As someone with coding experience and interest, you have a unique path to infosec that so many companies want, but find it extremely difficult to hire for.

Any company that ships software has to consider the security of their application - full stop. Most rely on scanners or annual third-party vulnerability assessments for this, but obviously that falls short. They need people who can build security in from an architectural standpoint. Someone who can actually implement the fixes suggested by the above methods, and ideally, someone who can help implement security as an integral part of the SDLC instead of as a bolt-on premise.

My recommendation is to make your way through 24 Deadly Sins of Software Security and The Web Application Hacker's Handbook. If you can understand the bulk of concepts in these two books, you'll be leagues ahead of almost any developer you find yourself up against in a hiring scenario. For the coup de gras, learn about threat modeling. It's a great way to teach other developers security and to build security into any system from design. Check out this book which is actually probably a little too comprehensive, use this card game from Microsoft (it seems silly, but I promise you it works), and watch this talk one of the guys on my team gave at BSides Cincinnati.

If you have any questions, PM me.