Generally the most expensive part of your HVAC system is the air compressor but it can vary depending on the type of system and its components.
In a central air conditioning system, the air compressor is typically the most expensive component. It is responsible for compressing and circulating the refrigerant that cools the air. Compressors can be expensive to replace, especially in larger units.
In a furnace, the heat exchanger is typically the most expensive component. It is responsible for transferring heat from the combustion gases to the air being circulated throughout the home. Replacing a heat exchanger can be expensive due to the labor involved in accessing and replacing it.
In a ductless mini-split system, the outdoor unit or compressor can also be the most expensive component, as it contains the refrigerant and compressor.