I have always been into exercise, but gained a lot of weight a few years ago and have spent the past couple of years losing it and getting back in shape.
By the way, I'm a living example that diet is more important than exercise for losing weight. At my heaviest (and I was heavy), I ran over three hours per day but also had a cake-making hobby!
My trainer (excellent and highly qualified) thinks that cardio (like running, cycling) is not the best use of exercise time but I enjoy it and think it helps a little with my weight loss so still do it at moderate to high intensity three or four times per week for 40 minutes to an hour.
I do agree with my trainer and the physio (I had an injury and needed serious rehab) that strength-training and functional work (bodyweight stuff) has been particularly effective. I also do yoga and pilates for mobility and targeting auxiliary muscles that are often neglected in weight-training. Building muscle has increased my fitness a lot and as a result, I can exercise more and at an intensity where it does aid weight loss. I also see evidence that having more muscle burns more calories.
All that said though, you can't go wrong. The physio, doctor, trainer all say that the main thing is to move. As another commenter already said, do whatever you can continue to do. When your fitness increases, you'll find you can do more. Don't feel like you have to achieve an Olympic level of training right now. Just get into the habit of moving more. Good luck.