If you are significantly overweight don't worry about working your lower body. You are already working out your lower body, because you are lifting your own body weight with every step you naturally take. To limit stress to your ankles and knees, work your upper body! You don't need weights to start, do Wall Push-Off's rather than Push-Up's.
Have low impact equipment at home, for bad weather days, or those days when you don't feel like leaving the house to work out. To avoid burnout, injury and stress to joints, opt for an Elliptical Trainer. Set it up in front of a window or TV, and go for it. No traffic, no dangers, no hassles. Elliptical Trainers are easy on your body, effective, and available for under $100.00.
Imagine our Metabolism is an Engineer stoking a Furnace, first in as fuel is the Sugar, then the Starch, then the Fats. Stored Body Fat goes in -- dead last. This is why a High Protein, Complex Carbohydrate, Low Fat Diet works best, for steady -- yet rapid weight loss. Adkins, Paleo, Hunter Gatherer Diet.