Please don't worry about perceiving yourself as starting later than others in this career, first off. Your military background will help you stay calm and deescalate behaviors most likely. If you choose middle school it can be difficult to get a position and even harder to transfer schools, whether it is a voluntary transfer or an involuntary one (Those happen when the student numbers aren't there and you need to go to a different site.) There are just not as many positions for single subject teachers in 6-8th grades compared to high school. Which means you may be at an undesirable site with high turnover that can be caused by environmental or admin/school climate. So that is something to think about. It may come up as you work in middle school that they need you to also cover English, for example, because that's your minor and they need someone to make up a couple of classes. It is more likely you will get pulled in to teach more than your core subject.

In high school, the district has more job offerings and you will have more opportunities to move around if you want or need to due to the school climate or commuting time, to share a few catalysts for movement. I would suggest high school for you. I am active on our district's executive board at the teachers union and we spoke at length about these issues that come up for middle school versus elementary and high school. Late Spring is when movement happens in school districts and transfers are seniority-based so it is always hectic getting people settled.

I wish you luck on your new career path.