Your breathing will find its own when you get healthier. Practice in thru the nose and out thru the mouth.
I start with shorter bursts and longer rests. So 30sec exercise and 30sec rest, when thats easy 30sec exercise and 15sec rest...keep increasing slowly. Good luck, you will get there xx
jumping jacks are a pretty intensive cardio evem for someone who is fit. try lighter but longer cardio workouts outdoors. i love the cross trainer at my gym, i could go for ages without a timer. by the way i quit smoking 60 a day 8 weeks ago and now my breathing is a hell of a lot better. no wheezing anymore when walking fast.
Start slow. A little cardio each day will help your lungs grow stronger. Maybe try jogging-- a couch-to-5K routine would be beneficial.