Dieting with a teenager in the home…

Hi there. I am a single Mum (yes a Brit) with two teenagers including a 15 year old boy who sounds similar to your son! We all like different foods so this is something I am very used to and your message resonated with me. The first thing I would say is that it is not clear which situation you want help with. Is is with 1) trying to get your son to eat more healthily ? Or is it with 2) budgeting for your different needs ? Or is it with 3) trying not to eat the 'unhealthy' foods you buy for your son ? (Or all three, like for me).
My advice for each would be :
1) Set some rules and tell him why. Your son isn't going to drink water if there is juice and soda in the house (I share your struggle). My son is allowed one small glass of juice in the morning to wake him up and then has to drink water for the rest of the day. He has to have veggies with every meal even if it is the same few on rotation. I only buy wholemeal bread - at first he hated it of course but has now got used to it and doesn't even notice it, He gets one junk meal a week (frozen pizza or fast food, snacks, soda etc) on a Friday evening and otherwise he only gets to eat junk if the whole family is eating junk. I do buy a couple of packets of cookies and a bar of chocolate for him to snack on during the week (ones that I don't like so I'm not tempted). I don't worry about white rice or ground beef and I plan meals with these ingredients. He doesn't have a lot of healthy food that he likes but I still stick with the healthy ingredients he does like and don't worry about variety - he'll get to that when he's older. I also am teaching him how to cook the sorts of meals he likes - he likes ramen for example so I am trying to learn and pass on how to cook a healthy version. It has taken us a while to get to a place where I am relatively happy with his diet (or at least not so worried). The important point for me was to actually decide to step up and devote some time and energy to this issue. I know what it's like as a single mum - you have to pick your battles. I picked this one at one point, it took a while but I didn't let up and now his diet is on track, he has new habits, I do too, and we're all happy. I will say that none of the rules are mean. It felt at first like they made him unhappy but I explain every day about healthy choices, empty calories, harmful industrial practices, my limited budget... and he does understand. Plus I'm the boss !
2) The thing that has helped my budget, and my son's diet, the most has been meal planning. I used to buy too much food and a lot of it would end up in the bin because without a plan in place for when I was going to cook that specific ingredient and what I was going to cook with it, I would get to the end of the day, exhausted after a hard day's work, knowing I had to make a meal but with no time or energy left to make a decision about what to make so I would end up cooking the quickest thing which most often is also the unhealthiest thing. And the fresh food I had optimistically bought in a more relaxed state on the weekend would just sit there going off. Now I sit down and plan all our meals and I am now used to thinking ahead and getting ahead with meal prep (defrosting this, soaking that, marinting the other...) so that I can get straight on with cooking instead of just staring into the fridge blankly for ten minutes before opening a jar of pasta sauce. When I plan the week's meal I choose budget friendly ingredients and because I no longer buy as much processed food, snacks, sodas etc (which all cost money, are very quick to eat but don't fill you up) and because I no longer over buy things like fruit (I know that I won"t need more than 5 or so pieces of fruit for the whole week whereas I used to buy whole bunches of bananas and dozens of apples) basically my budget has decreased. I think if budget is limited, quantity should be reduced before quality so I really try to get good quality fruits and vegetables and meat. I buy organic white rice in bulk etc. I always buy the cheapest versions of any household items or products that we are not going to actually eat though.
3) I have set rules for myself too. I don't eat the same thing as my kids any more. They are growing and need more calories and I am trying to shrink and need fewer calories but I need to feel full. I always eat porridge for breakfast. I eat an enormous salad for lunch and I make sure I have salad and vegetables on my plate in the evening and I just eat less of what the kids are eating. I weigh everything and never put more than 100g of carbohydrates on my plate. I put loads and loads of salad items and make sure I get enough healthy protein. I no longer use salad dressing or oil. I mix together soy sauce and vinegar and, sometimes, add the smallest amount of a chinese black-bean chili oil. I find with these strong flavours I don't need oil-based sauces. Basically I never allow myself to go hungry because that is when I will snack. And how I do that is by eating a lot of vegetables. Things like cucumber, zucchini, broccoli, carrots, bell pepper, spinach are all delicous cooked or raw, they are all cheap and they are very filling. They are always the first thing I put on my plate for every meal apart from breakfast. It's a new habit and it's working.
I hope this message is helpful, hopeful and kind.
I say that anything worthwhile takes time. It's not easy being a single mum. It's not easy parenting teenagers. It's not easy changing habits or losing weight. Nothing and nobody is perfect.
But... happiness is progress and that's the message : progress is always possible !