I'm applying to the Navy Nurse Corps currently and have every intention to work as a psych nurse within the Navy. The military branches are a great route if you're looking to work with current troops; the VA is a great way to work with Veterans. You can go into the military as a nurse if you have a BSN (don't need your masters but through the military you may get the opportunity to earn your masters or DNP). With the VA I believe you just need an ADN or a BSN and once again you'll have the opportunity to continue your education and make an even greater impact as an NP.
Personally I've done a clinical rotation at a VA psych floor and they need people who care passionately about mental health issues and especially those issues pertaining to PTSD because it can be very easy to burn out. I hope we can look forward to making leaps and bounds in the care of those troops and veterans living with mental illnesses in the future.