Very interesting case.
My first inclination is to say when you are a student if your family is nearby live there (assuming you can tolerate your family, and it sounds like you have a good relationship). This can work well when you are a bit older and have already had your "away from home" time, which fits your case. My brother actually did this during his masters after being away for his BS. A friend of mine actually did this during his first few years of employment (that paid extremely well actually) after being away for college. It can be an enormous savings vehicle early in your career. When you are young savings make the biggest difference because money has the highest opportunity cost early in your life (it will grow for longer) and typically money has the highest marginal utility as well (your income is low early on).
Obviously I think most people don't want to move back in with their parents, and for your generation it has become an almost cliche mark of "failure". But you aren't a spoiled kid who got a Medieval Art History degree on $150K of student debt and now lives in the basement holding out for a job that will never come. You are a successful person who has already made a difference and is making excellent and pragmatic financial decisions.
I'd hesitate to buy in your situation, it seems like you'd be selling within five years. Keep in mind the high transaction costs of real estate. Though if buying from your dad these could be greatly reduced, and factor that in if you do purchase from him - typically he would pay a 6% real estate commission that the two of you could avoid so there is money in reduced price for the two of you to share guilt free. Remember, though, that these are a seller responsibility and you will likely pay them when you sell to a third party later. You do probably have some good benefits in mortgage options coming out of the service, but also keep in mind for the next few years you will have vanishingly small income and so you will actually get no mortgage interest deduction (i.e. you will be taking a standard deduction, so property taxes and mortgage interest really aren't deductible). That's going to tilt the rent vs. buy decision a bit more towards rent compared to a higher income earner with a more expensive house. State income taxes are also deducted on Sched. A so how much of a true mortgage interest deduction you get is dependent on how much state income tax and property tax you pay. If you aren't familiar with standard vs. itemized deductions now would be a good time to become familiar with that topic, low income folks buying lower priced homes often get sold on buy vs. rent because of the "fact" that mortgage interest is deductible when really for low income/low house price this is often not true at all. It turns out the mortgage interest tax deduction is actually a regressive tax, that is it benefits high income earners much more than low income earners. Despite that fact real estate industry members often try to sell it as a benefit to low income earners.
Also keep in mind the life transitions going on. I'm sure entering the Army was a huge change. Leaving it likely will be as well. Being a student is a different life and mindset from having a job, so you will have another transition in a few years. While I haven't done the military service thing myself, I have yo-yo'd through a fair number of transitions from student, to over worked and highly paid employee, back to student, to government job in the middle of no where, to married with two decent incomes owning a big house, to renting a townhouse with two excellent incomes, to a too large house in preparation for a family with two excellent incomes. Each of these transitions was an opportunity to change my housing situation as there were so many other changes going on that it is just natural to adjust to a new housing situation. With that in mind you might consider whatever you choose now is going to be different from what you will chose when you finish school. Living with your family might be just the right kind of change for a few years and it is of course economically advantageous. I also know that when my brother lived at home it strongly encouraged him to get out of the house a lot. As a new student just coming out of the army you might very well want to be spending more time out in the community at large, finding nice external study haunts and groups. So maybe a room at your parents would be just fine since you will be doing little beyond sleeping there...
Anyway, you seem to have your head wrapped around the various options well and they are all pretty sound. I'd put my vote in for stay at home, but that of course depends a lot on how you feel about that and you will be the best judge. It is clearly the best economic decision, but so is living in cardboard box in the park. There are limits.
