If you want cybersecurity with web application testing (with overlap to mobile application testing), begin with The Web Application Hacker's Handbook. Best single treatise on the subject.
You should look through this entire thread:
https://www.reddit.com/r/netsec/wiki/start
I also highly recommend the OSCP (Penetration Testing with Kali Linux) course and Cody Brocious' (daeken's) course called Breaker101, at breaker101.com.
Good luck.
For a little more complete reference I point folks to 'tptacek's list at http://amzn.to/cthr46
For offensive computer security:
http://www.cs.fsu.edu/~redwood/OffensiveComputerSecurity/lec...
This is a very nice reddit comment that explains some of the various foundational, necessary knowledge and where to learn more about them.