A good fat-burning exercise is squat-to-curl-to-press (shoulder press)...you can use this exercise as a combination strength and cardio exercise. The exercise is done just like it sounds: squat, bicep curl and shoulder press (that is 1 repetition).
Any full body exercise will give you more fat-burning benefit than a seated exercise. For example, standing shoulder presses will give more fat-burning benefits than seated shoulder presses.
The squat-to-curl-to-press is also a compound strength exercise. These types of exercises work major muscle groups which helps build more muscle and burn more fat. You will also maximize your time during your workout (fewer exercises with maximum benefit). Doing too many single joint exercises like calf raises, bicep curls and tricep extensions is not a good use of time and you get little benefit for the amount of time spent.
The squat-to-curl-to-press will also work your core area. Keep your torso braced (like taking a punch to the gut) throughout the exercise.
"Exercise is not my life.....exercise makes my life better!"