I'm Meg, nice to meet you.
The best exercise program for fat loss is one that includes both cardio and strength training.
Cardio is any exercise that raises your heart rate for a sustained period of time, so that would be your treadmill, elliptical, stairstepper, walking, running, swimming etc. It doesn't matter which piece of equipment it is (or no equipment if you're walking or running), just as long as you elevate your heart rate. Cardio will be your main calorie burner and will strengthen your heart and lungs (cardiovascular system).
Equally important is strength training (weight training, weight lifting etc). It's very important to maintain and build our muscle mass while we're losing fat. Muscle is the furnace that burns calories, so the more muscle you have, the more calories you burn -- awake or asleep, 24/7/365. Muscle will also keep your metabolism elevated so that you can lose fat and maintain at a higher calorie level. And it will ensure that you get to goal in a smaller, tighter body.
So my suggestion is to find a kind of cardio you like (walking on the treadmill is fine so long as you're elevating your heart rate) and putting together a strength training program using the equipment in your gym. As for when you go back to school in the fall, do you have access to the school's gym?
Hope this helps a bit!