That's fantastic Kate. A regular program of exercise is beneficial under any circumstances, but especially yours. You've been under the weight of much stress lately and kicking around some iron is a great way to burn it off.
Exercise releases endorphins that help with depression. http://www.webmd.com/depression/guide/exercise-depression
For maximum benefit, utilize the training staff on hand to help you set up an organized routine rather than just wandering around the gym hitting random machines. It will help you stay interested in what you're doing, even during the hard parts, and you will see results faster.
I've been a gym rat for several years and I love it. I love the way it makes me feel.
And remember: You can't out exercise a bad diet.