This is a great place to start, and gain a lot of great experience. Nevertheless, learn everything you can learn about the providing services to the clients and of the shelter system, and MOVE ON.
Don't get trapped in the daily drama of the staff around you, because you will be surrounded by pettiness, foolishness, gossiping, at times unfair treatment and unprofessional-ism: it does not matter.
Management many times will appear under-qualified to be part of the upper administration (and some really are under-qualified), but again learn whatever you can, such as which management skills you should NOT use in the future. You will feel very unsupported by management, because all they seem to care about are client placements into supportive housing and filing the charts. It is okay. Let those experiences build your character, and help you grow as a leader; do not get caught up in it.
Stay 1-3 years here at most, and move on. It will hurt to leave some good friends you leave behind, but it's part of life and you all will stay connected.