When you put your shoulders back, make sure your not actually tipping your torso back! Doing this sends your legs slightly forwards! Ask your instructor to check throughout the lesson that you are sitting up straight! Make sure you have your weight gently in your heel- don't force them down! This will help keep all your weight under you!
Tying your stirrup leathers to your girth might be a bit risky. If something were to happen, your stirrups would be tied down, not loose "freely" (which is safer and gives you the secure feeling). For example, if you fall your foot might not come out, and result in dragging or worse (I speak of the dragging part from experience- NOT FUN!).