First, kudos on taking the first step toward dealing with your weight. Second, although time at home may appear too busy, all you need is 20-45 minutes to get started with an exercise program.
With that said, the key to weight loss is to simply burn more calories than you consume. So, diet is key. Focus on fruits, vegetables, lean meats and low fat dairy. You must minimize sugar, starches and the fast food.
Next comes the exercise. Perform the cardio of choice (walking, swimming, cycling, etc) three times a week for 20 minutes. This may mean getting up a bit earlier or investing in a cardio machine. You should also weight train three times a week as muscle burns more calories than fat. All this can be accomplished with a pair of dumbbells or elastic bands and a stability ball.
For detailed workout programs and meal plans, check out the fitness model program at: http://intenzathletix.com/likes/fmp.
Good luck!