Let's start from the beginning. Just to set the stage, with the exception of a TA position that I held in college, every job (summer job, co-op, internship, full-time position) I've ever had has been in the defense industry, either as a government civilian employee or at a defense contractor. In addition, I've only applied to one job outside of the defense/intelligence sector. I'm planning on spending my entire career in this industry.
The notion that employers aren't allowed to talk about what they do is incorrect. I was a candidate for a position at a Department of Defense intelligence agency that specializes in signals intelligence, the protection of US communication and network systems, information security, and cryptography/cryptanalysis. At the time of the interview, I did not have the appropriate clearance to even enter their primary facility - I was interviewed off-site, in a remote location, and couldn't go much beyond the lobby and interview areas. However, I was able to ask questions about the type of work I would be doing - the office environment, the tools and technologies, and the problems being worked on (or problems representative of those being worked on). Often, it's not the problems that are classified, but the solutions to those problems and the capabilities generated. I was able to learn enough about what that particular team did to say that I was not interested in the position for moral and ethical reasons.
During the application and interview process, you should be able to learn enough about the position to be able to make an informed decision about what type of work you will be doing in the job. And learning about the work environment aspects of the job would be the same as any other job - ask about culture, benefits, opportunities for growth and development. In a government agency, those are often public information since it's consistent across agencies and departments. In a contractor environment, they'll be more than happy to discuss those things, since that's typically an HR topic that applies regardless of the project or program.
In terms of politics in the office, I've never encountered that, and when talking to friends of mine outside of the defense industry, it seems pretty similar in nature. I would suspect that this is more of a corporate culture thing rather than something that can be generalized to the defense industry or government contractors.
Security at work varies. Most places will provide people with an unclassified workspace in addition to workspaces in classified environments. At my desk, I have nearly free access to the Internet. However, in a classified environment, you don't have this access. Much of the work that I've seen done actually happens in unclassified environments and is then brought into classified environments because the actual, real-world data that the systems operate over is classified. The system itself might be proprietary, and sometimes even open source.
As far as getting a security clearance, the forms are somewhat time consuming. You need to often recount your jobs, addresses, friends, colleagues, and family going back 5-15 years depending on the type of clearance investigation. Depending on some of your answers, there might be interviews, polygraphs, and questionnaires to fill out. You can see the forms online, such as the SF-86 (PDF here), which is used for DoD Secret clearance (and perhaps other agencies as well - I'm only familiar with DoD).