Well I don't know about inexpensive, just about every heat source is going to cost you, except portable electric heaters. My preference is radiant heat. You can install a water heater, very much like a water heater for heating your domestic water and use it to run some baseboard heat around the outside walls. The system will need a small expansion tank, pump and zone control valve attached to a thermostat. You will then have an independent heat source for the lower level. The water heater can be electric or gas. Or you could just go with electric baseboard heat. Again independent control.