Seems 1200 cal AND exercise is a bit much. Too few calories to burn. You may feel weak during and after exercise. Maybe ask dietician?
You may find that - depending on your general condition - SPINNING burns the most calories and gets you an unbelievable happy high. But careful not to overdo it.
Gyms can be intimidating (have been there) but once you get a rhythm going you'll blank silly people out.
I found dancing, swimming (yes, in a swimsuit in public), pilates, and running outdoors in the woods the best. Had number of personal trainers before finding THE BEST!
Vary every few weeks - otherwise you get bored. Have gone from size 18 to 12-14 last years. But preganant now and slowing down.
Enjoy moving and don't let the skinny bunnies annoy you.