The actual answer to your question is low intensity aerobic activity, after a period of fasting (so first thing in the morning). The real question, however, is this — is that the most efficient and effective approach for your goals? Assuming your goal is to lose body fat — I would say absolutely not!
Its not about how many calories you burn while exercising, or what percentage of those calories come from fatty acids as fuel. True body composition transformation comes from the number of calories you burn the other 23 hours of the day. We burn predominantly fat at rest, so the question is how do we burn more calories/fat at rest? The calories burned while exercising are relatively small and insignificant compared to that number.
The answer is to increase your resting metabolic rate. The amount of lean muscle you carry is positively correlated with resting metabolic rate. Your best approach is to strength train, build some lean muscle, boost your resting metabolic rate, and burn more calories at rest. The body burns fat as rest like I said, but as the intensity of the activity increases, it starts to burn more glucose. During high intensity activity, the body is deriving 100% of its energy from glucose. So during strength training, you will actually be burning more glucose than fatty acids, but this is exactly what you want (although it might not seem so on the surface).
High intensity strength training causes microscopic damage in your muscle cells. To repair this damage (in the recovery process) requires energy. This repair happens in between training sessions, not during. And what are we burning in between training sessions at rest? FAT. Your body will burn fat in the recovery process from strength training, a hell of a lot more than doing one our of non-challenging aerobic activity.
That just scratches the surface. Strength training also has positive impacts on growth hormone secretion, which is our primary fat burning hormone. Just remember this, fat loss is not about how many calories you burn (or whether or not those calories are coming from fatty acids) its about the metabolic and hormonal responses to exercise. These are far more dramatic with glucose-burning strength training than fat-burning aerobic activity.
To put into practical terms for you:
1. Strength train 3-4 times a week for hormonal release, to build metabolic-boosting lean muscle mass, to cause muscular damage that is energy-costly to repair from, and maybe to look cool in spandex
2. Don’t worry about what exercise modes burn more fat. That’s meaningless. You will burn plenty of fat at rest assuming you are in a relative calorie deficit, and your metabolic rate is high (from consistently strength training).
I hope that makes sense, no time to edit, heading to a training session. If you have follow up questions fire away.