Counting calories is definitely a frustrating and futile process. Instead of exercising to burn a certain number of calories, exercise for a set amount of time or until you can get all of your lifts out. If I were you I would shoot for about 20-30 minutes of INTENSE cardio 2-3 days a week and do weights three days a week. The weights are going to help you more than the cardio as the more muscle you have on your body, the more calories you naturally burn each day. Plus, weight trainging helps to you burn calories throughout the day while cardio really only burns calories while you are doing it.
For weights.. you really don't need to get too intense if youre just starting. Doing simple things like body weight squats, body weight lunges, step ups, pushups variations, dips, and inverted rows.
Remember, fat loss is about 30% exercise and 70% nutrition. You can exercise all you want but if you're not fueling your body properly you will ultimately fall short of your goals.
Hope this helps,