Since nuclear power plants were first developed over 80 years ago, most have had thermal reactors with enriched uranium as the main fuel. As a result, huge amounts of depleted uranium must be stockpiled and stored. Fast reactors operating in breed-and-burn (B&B) conditions are one potential approach to reducing the need for storage facilities to hold spent nuclear fuel and maximize the effective use of uranium resources. Sustaining B&B operating conditions depends on the choice of core materials. Here, we perform neutron balance analyses to determine the best combination of fuel and coolant material. We identify the features of the reactor core needed to maintain B&B operating mode by the amount of neutron loss from the core and coolant heat removal capability. Finally, we demonstrate that a large or small sodium-cooled fast reactor core with metallic or enriched nitride fuel, respectively, can sustain the chain reaction and B&B operation mode.