Lauren, the treadmill is an excellent calorie burner but you need to walk to get your heart rate up and keep it elevated to burn fat. You can also do interval training doing a walk-run-walk workout which also burns a lot of fat.
As for weight training if you can get someone knowledgeable or even better a personal trainer for a session or two to show you around the gym that would be great...
You can start out with machine workouts for 4 weeks then work yourself up to working out with free weights. To start you should work out doing more compound exercises squats for legs, chest press for chest

, lat pull downs or seated rows for the back, bicep curls and triceps pushdowns for your arms... then some abs just basic crunches on a ball or on the floor is good... This should be a good starting point for a beginner and will get your ligaments and tendons ready for a more involved workout later on... Oh, and if you have time you can do this 3x/week either on the same day after your cardio or on alternate days...
Hope this helps keep us posted on your progress
