I have just started down this path myself. I hit the gym everyday, I started with 15 minutes on a bike, with a 3 minute cool down. Each week I am going to bump by 2 minutes. I am at 17 minutes now and I have already noticed that I am not out of breath when I play with my kid. I am starting slow and trying to make the best of it. I also work on a muscle group everyday. I don't wail on it, just until I can feel that I have made the muscle tired. 20-30 inclined situps, 3 or 4 reps on biceps with 20 lbs or some legs. Like I said I am not trying to kill myslef.
My doctor told me something that may help you understand your body a bit better. Fat is almost perfect in its construction. It takes almost no energy to store, and similarly little energy to create. Lean muscle takes a ton of energy to create and a bunch to maintain. You don't need to bulk up on muscle to replace fat, but once you have more toned muscle you will burn more calories quicker.