Things have changed now, most of the companies management is Aware that Security testing should be included as part of Testing.Many critical Banking Applications, E-commerce Websites which stores customer Credit details have to oblige to PCI compliance.
To me, it's really interesting field to Dig bugs that may break down your systems and can get access to sensitive Customer Information or may bring down your systems for a While.Definitely, it will be an Asset for you to learn Penetration testing concepts and to hold a recognised certification.
Where to Start:
If you got no idea about Attacks and Vulnerabilities then start with Cybrary IT this is the place where you can watch lectures on Security concepts for free.
Learn more about OWASP, OWASP Top-10 attacks and their consequences and you feel that you're equipped with concepts of security testing and attacks then start implementing them, testing them practically here
Once You get practical hands on knowledge on finding vulnerabilities in an Application and implementing security attacks then you may think of tools and browser Add-on's. I feel it's too early for you to play with tools better to learn and implement things before playing around.
To get inspired more sign up to newsletter's of these websites which sends you a daily email of Current Security Hacks happening around.
The Hacker News
Hope this information helps you to get started.