While serving in the military might help you develop knowledge of tactics (the art of winning engagements and battles), it is unlikely to give you much of an education on strategy (the science of winning wars) unless you get a chance to go to a war college and actually study strategy (and that basically requires you to be an officer).
For a good study in military strategy, you need to read history books - lots and lots of history books. There are some essential texts in military science - Sun Tzu, Clausewitz, Mahan, and so on - but they generally speak of platitudes and generalities, rather than detail how real campaigns have been won or lost.
I can't really recommend any specific books, but finding books on the American Civil War, the First World War, the Second World War, the wars in Malaya, Vietnam, and Algeria, and the Persian Gulf War would be ideal, as long as these books actually cover the high-level decisions and constraints (such as geography, weather, logistics, coalition relations, morale, public opinion, and so on). Other wars would be illustrative as well, but these wars would be good starting points for an understanding of modern strategy.