What types of psychology should I focus on if I want to help treat military personal?

What a noble career path- good for you! You will need at least a Masters Degree in a Counseling or Psychology major, preferably a Doctorate...as having a Doctorate will help you navigate around a lot of red tape. The VA is moving in the direction of being more accepting of Master level clinicians but the process has been slow. If you want to finish at your Masters Degree (as opposed to getting a Doctorate) you'll want to be looking for a Masters program that has something called CACREP accreditation. Right now TrICARE (this is the "veterans insurance plan" that pays for their counseling) only reimburses Master level counselors who graduated from CACREP schools (worrying about all of those details is far less necessary if you have a Doctorate, but a Doctorate is much more expensive and time consuming to acquire). In terms of topics of focus for school....Vets are people just like anyone else, they experience the same problems as everyone and you'll learn the same psychological theories and practices as everyone you go through school with. Post Grad training in trauma treatment would be very helpful for working with vets. There are many, many different theories/ treatments for trauma and you will be exposed to the big names in the field during grad school, that exposure will guide you toward what you feel is a good fit for you.
This is a great field to be in if you love people, the rewards can not be measured in dollars and I enjoy my work immensely. Best of luck to you!

My knee-jerk response would certainly be PTSD. However, to get a more precise answer, go visit the VA hospital nearest you. Ask for the staff directory and call on the person that fits the most likely position and tell them what you’re after. Offer to buy them a coffee and/or explore volunteer opportunities to help them out.
Hope this helps,
-rbt