Definitely check with a doctor before doing anything that internet strangers tell you, but my guess is that you're going to want to focus on low-impact exercises. I agree with this anon >>27
that swimming is probably the best option. If you don't have access to a pool, then a rowing machine may be a good choice too. Rowing is no-impact, and you can make it work for both cardio and strength training, depending on what sort of effort you put into it. It's also nice that you can stick a rowing machine in an air conditioned room, and lots of them use your movement to spin a fan which blows cooling air on you.
In addition to working out, you're going to need to get calories under control too. At my heaviest, I was 230 lbs, and I worked my way down to 165 lbs. I expected to need to spend every day in the gym, and honestly, I quickly found out that I didn't need to. Pick any exercise: running, swimming, biking, it doesn't matter. Find one of those online calculators for how many calories you can burn in an hour doing that. A real hour of working out, not thinking about doing it for 10 minutes, then warming up for 15 minutes, then taking a break, then going with a bit of intensity for 20 minutes. No, all-out going for it for a full hour. What you'll find is that it's a ton of effort to burn maybe 600 to 800 calories. Comparitively, how easy is it to just stop drinking soda? Stop eating chips. Stop putting sugar and cream in your morning coffee. You can save 1000 calories a day, easily, by watching what you eat. I dropped almost all of my weight by building up my discipline with food, not by building up my body with exercise (that came later). If you can do both, that's even better. But if you have to choose one, go with the diet option. It really is the path of least resistance. I aimed for between 1200 and 1400 calories a day. With a daily expenditure of about 2200 calories, I was at a 1000 calorie deficit per day, which makes you lose 2 lbs per week. This was achievable without going overboard. If I had tried to do any bigger of a deficit, I wouldn't have been able to keep that up for the couple months that I did. Losing a ton of weight is a marathon, not a sprint. You need to put together a plan that is good enough to make you lose weight, but is also realistic and comfortable enough that you'll stick with it for a long time. Take a good look at the /fit/ diet image in the OP. Try to put together a meal plan from those options that comes out to about 1500 or so calories a day. Maybe something like 2 eggs and black coffee for breakfast, a grilled chicken breast and protein shake for lunch, and fish with rice, broccoli, and water for dinner. Don't put sauce on anything, it's a waste of calories. If you need to improve the taste to make it palatable, use dry spices and herbs. They have no calories, and they make things delicious. Pepper, paprika, basil, oregano, rosemary, thyme, parsley, garlic powder. They can become your new best friends. Keep in mind that vegetables are super low in calories, while full of vitamins and minerals that are good for you. Also keep in mind that not all calories are created equal when it comes to making you feel full. Think about eating 400 calories of either cake (mostly calories from fat), 400 calories from a loaf of bread (mostly calories from carbs), or 400 calories worth of soda (calories from sugar). You'll be hungry again in no time, and in the case of the soda, it won't do a single damn thing to make you feel full. Now think about eating 400 calories worth of steak (calories from protein). You'll be satiated for hours. This is one of the reasons /fit/ people advocate high protein diets while you're dieting. It is much easier to stay at a calorie deficit if your food choice doesn't actually result in you being hungry, compared to feeling like you're starving every day.
What I want you to do is put together a diet and exercise plan. Come up with a few preplanned meals, with set serving sizes, and do the math on how many calories each of those meals is. Draw your options from the /fit/ diet image. This will be your menu. Every day, pick whatever you want off of your menu, but be sure to keep your daily calories count to 1500 or less. Use plenty of spices and herbs to keep things tasty. If you're miserable with your menu choice, you won't stick with it. Weigh yourself every morning, at roughly the same time. Keep track of it in an excel spreadsheet. You may not notice much of a change in your weight day to day, but week to week you definitely will. Do what you can to exercise, but focus your attention mostly to dieting. One month after your first day on this new plan, make another post on this board and tell us how much progress you've made. You won't be done after 1 month, but you'll be on your way. And if you can keep it up for 1 month, then you can keep it up for 2. And if you can keep it up for 2 months, then you can keep it up for 3 months. And if you can keep it up for 3 months, then you have the discipline and the tools you need to reach your goal. It only becomes a matter of time.
You're going to make it, anon. I believe in you.