Why don't you just go for regular bike rides or go for a power walk, leading up in time to a jog. You don't necessarily need to buy any expensive CV kit.
If you want something to use at home, buy a good quality mini trampoline, a set of dumbbells, workout bench (optional) and a Swiss ball.
Spend 20-30 minutes 3 -4 times per week doing your Aerobic exercise, which will help to get you get fit and burn calories. For your body to use excess fat as fuel, you do need to do a balanced resistance workout, using either weights, your own body weight or both. The more lean muscle you carry, the more fat will be burned and your metabolism will increase.
Unfortunately you cannot spot reduce fat from any particular area, it will go from where it will go and stubborn areas like the stomach are usually the last to go.
Start off with 2 sets of 12 repetitions of the following.
Dumbbell Chest Press OR Press ups
Dumbbell Single Arm Rows
Dumbbell Shoulder Press
Swiss Ball Wall Squats with Dumbbell Front Raise
Swiss Ball Hamstring Rolls
Static or Dynamic Lunges (Alternate Legs)
Swiss Ball Stomach Crunches
Heel Taps (For lower abs)
It is important to change your routine every 4-6 weeks, to avoid your body adapting (getting used to) the exercises you are doing.