First of all, congratulations on 2 things: serving your country and having the intelligence to think about your financial future.
I wish I had the same financial mindset back in my army AD days. Being an enlisted, we don't get much. One thing a lot of young recruits neglect to sign up for is the GI Bill. They don't look at the positive side of this. I heard that for educational benefits, the government pays more than it used to in my days which was only 70%.
I think the minimum contribution to Roth is $100/mo., I don't know if there's a minimum initial deposit. I don't know a whole lot about TSP. Overall saving money rather than wasting it on booze while off duty is much better.