CMOS inverter propagation delay
The propagation delay depends most significantly on the load capacitance, which is gate capacitance of any transistors that are driven by the output signal as well as the capacitance of the wiring that connects them. As you said, the propagation delay also depends on the power supply voltage.

The propagation delay for an inverter is not really dependent on the input capacitance of that inverter, but it is dependent on the input rise and fall time. Since the input rise and fall time would be dependent on the input capacitance in any real circuit, I guess you could say that the input capacitance of the driving inverter is relevant.