There are many possible ways to answer this question. I would argue that the main way in which Washington shaped the future of these institutions was by, in a sense, weakening them both.
The first thing that Washington did was to emphasize the idea that the military should be subordinate to the civilian government. Washington did not try to use his popularity with the military and his influence over them to put himself and the military in power. This was shown most famously in his actions to quell the “Newburgh Conspiracy.” When he did so, Washington instilled in our military the idea that it was subordinate to civilian government.
The next thing that Washington did was to emphasize the idea that political leadership was vested in institutions, not in individuals. This happened when Washington stepped down as president after two terms. He did this instead of holding power for life, as would have been easy for him to do. By doing this, he instilled in political leaders the idea that the system was bigger and more important than any one person.
We can argue that, by doing these things, Washington saved our country from some very serious ills. We did not descend into rule by a series of military strongmen as happened in so many other countries that became independent.