Musekinin Kanchou Tylor, Gate: Jieitai Kanochi nite, Kaku Tatakaeri Recommendations
The Irresponsible Captain Tylor's warfare is of the intergalactic variety, where as Gate's is a mixture of modern / medieval fantasy. But what links the two is the manner in which slacker main characters unwittingly find themselves promoted in the military and in charge of others after actions they themselves did not perceive to be that much of a big deal. And how they then proceed to become increasingly famous as heroes... despite having little to no motivation!
The tone of the two series is also very similar: comedies with a harem-ish edge. Gate is more otaku pandering in this regard, but Tylor also has females