You can burn fat and lose weight without ever going to a gym. Just make sure you use your home gym on a regular basis! You can easily reach your weight loss goals working out at home. I train the majority of my clients at their homes or places other than gyms.
What do you need in your home gym? Your body would be the first thing you need. Most of your exercises can be bodyweight exercises. Just add in a stability ball, dumbbells, resistance tubes, workout bench and you have all you need to workout.
The key for you is probably to speed up your metabolism. Building muscle mass will speed up your metabolism because your body has to work harder to maintain more muscle. Muscle mass will also cause you to lose body fat and inches which is more important than losing weight (the weight loss will take care of itself). This can be done best by doing full body resistance workouts 3 days a week and intense cardio exercise 3 days a week.
Keep your body guessing by varying your workout routines and intensity. Do different lifts for the different body parts, such as substituting bench presses with stability ball dumbbell presses or doing lunges instead of bodyweight squats.
A shorter, more intense 30 minute full-body circuit weight workout will work better than a 1 hour weight workout when you are trying to lose body fat and weight. A circuit workout is one in which you do one exercise after the other with little or no rest between exercises.
Here is a good home workout that anyone can do:
Since this workout is circuit-style, you also get the benefit of a great cardio workout. Do each exercise (8-10 repetitions) one after the other with little or no rest between exercises. Rest 2-3 minutes and do the circuit two more times. Here is a good bodyweight workout:
--Step ups (with knee high bench)
--Pullups or chinups
--Triceps dips on bench
I have to say something about nutrition. Eat the foods that are healthy for you but also track your daily calorie intake.