If calorie burn and weight loss is your goal, running is definitely the biggest "bang for your buck," meaning it is the most efficient calorie burning form of cardio you can participate in. But that also should not be surprising because running is HARD. It takes a long time to build up your endurance to a place in which you can run long distances at increased speeds, and it takes a lot of training runs to build up enough stamina to run a race. So if you are new to running, you might be finding that it seems extremely hard. But my first piece of advice would be to stick with it! Yes, it will be hard. Anticipate that, but then push through because you will quickly find that it DOES torch calories and help lose weight.
Exactly how far you need to run to lose weight is dependent on several factors. You must first consider your own body, how much you weigh, how much of that is fat you can burn versus muscle, and what your metabolism is like. The more fat you have, the easier you will find it is to burn off fat because you have more energy to burn. And if you have a faster resting metabolic heart rate, then you will lose weight faster and running will just serve to increase that even more. And then there is the most important factor in all this to consider - your diet. It doesn't matter how many miles you run; if you are eating more than you are burning, you will not lose weight. Weight loss can simply be broken down to understanding that calories expended must surpass calories consumed. But you should be careful not to under fuel yourself either. Not eating enough will result in a slowed down metabolism that refuses to burn fat, which will stall weight loss. Steady weight loss to get you to your ideal weight involves moderate exercise and eating in moderation (but still eating enough!)
Starting out, I would slowly work up week by week, adding a half a mile of distance to your run each week. Aim to run 3-4 times a week, permitting your schedule. And as long as you are making wise and healthy food choices, you'll likely start to see weight loss in no time!