What are the best exercises for weight loss and burning fat? Would an elliptical machine be good for these purposes? What kind of program?

Aerobic + weight. A combo of aerobic (cardiovascular) +weight bearing (build muscles) exercises along with proper/balanced diet is probably the best, but some is better than nothing. In the US, the trouble is that we have too much..sodas, juices, pizza, donuts, brownies, cookies, truffles, ice cream, lattes, beers/liquor, and the evil of chips... So, be sensible. Stay healthy. Good luck.
Exercises, weight. Walking and aerobics are the most recommended together with good diet. Do not walk like to be going to a marathon , doing up hill , that will be increasing legs before loss weight and measure.Go to your primary care , good pe, bfc, and amount of pounds you need to loss will be recommended as per your age, stature, sex, general medical conditions, etc.