Hello, fellow member that was diagnosed with a hypothyroid @14 y/o. My highest weight was 260, I am now 180. I'm taking 0.175mg.
You're looking at the same approach to weight loss as anyone else, besides the fact that you should consume little to no Soy products and try to keep cauliflower and broccoli to a minimum. You should still eat them because they're extremely healthy and full of vitamins and proteins.
You will need to consume slightly less calories then the average person. I would go with 150 to 200 calories less then any website recommends you to. After that if you don't lose weight keep reducing the calories in increments of 50 until you're losing 1 to 2 lbs a week. You should be taking a multi-vitamin and good quality fish oils.
Lift weights 3 days a week, do cardio 2-3 days a week and eat as healthy as possible, consume lots of protein and stay within your allotted calorie amount and the weight will come off.