Simply going on a "diet" isn't the answer... In order to lose weight and keep it off, it's necessary to adopt lifestyle changes that you can maintain lifelong. What happens when we diet is that we, typically, change our eating habits to something we can't possibly maintain, so as soon as we go back to any kind of normal eating pattern we gain back all the weight we lost, often, plus more.
You don't say how old you are, but it's not good for anyone to be eating a lot of junk food. Since you mom doesn't cook, perhaps you could learn to cook some healthy foods for the family if mom will buy the groceries. If take-out is the only option, try to choose wisely and pick dinners that chicken, fish, vegetables and/or fruits and less things like potatoes/fries, rice, breads, etc. Also stay with smaller portions. You might also ask your mother to purchase things like fresh fruit and vegetables like, carrots, celery, etc that you can munch on raw for snacks instead of eating the junk food. You could also ask for things like nuts and seeds for snacks, but you need to go a lighter on those because they have more fat.
Also make sure you get plenty of exercise to help stay healthy.
Since you're 17 now, are you going to move out soon to go to college, or are you staying at home? If you're moving out, you have your solution -- you won't be around all this temptation and you can come up with a permanent way of eating that is healthier for you. You're also at an age where you can make your own meals if you do stay at home. But avoiding that junk food is up to you deciding to do so -- not every single day of your life, but most of the time. If you combine a good balanced diet of plenty of veggies, moderate intake of sweet fruits, whole grains, and fewer meals with red meat as the entree -- meaning something like legumes for your protein entree -- combined with increased output of energy not only in formal exercise but just by moving around more, your metabolism will slowly change in a permanent way and you'll lose weight and keep it off. It's not an easy thing to do, but your post suggests you want this change, and at 17 you are getting to where you will be responsible for yourself more and more so that should make it easier to do. How much do you exercise now?