I think you need to rephrase your question. Combustion usually goes to completion without any need for catalyst.  Catalyst could help you reduce NOx or allow partial oxidation at lower temperatures but I am not sure what you mean by using a catalyst to produce more energy.

The best catalyst are usually high cost. You eventually make an economic trade off of cost and equipment size. Platinum and palladium are often used in combustion with good efficiency. Notice that the catalyst is giving or receiving electrons to activate oxidation reactions. If you can isolate your equipment electrically, the electrons can in principle be provided by any common metal electrode charged negative (a cathode) with respect to another electrode  possibly made of carbon (anode). Oxidation occurs at the anode where carbon soot may reach equilibrium with carbon dioxide. It produces electricity and heat, plus carbon dioxide and water. You might call it a fuel cell where efficiency increases as the temperature rises.

Check out this recent publication

It depends on the type of fuel, the transitions metals supported are good to save energy in the combustion, but they are expensive and can suffer easy poisoning. The oxide compounds like ceria, zirconia present good catalytic activity, but the doping with other metals can improve the catalytic properties. The perovskites can absorb great quantity f oxygen on the surface but depend on the synthesis conditions in order to give better catalytic properties, the doping of them also is a good option.