Half of House Connected to Heat Pump, Other Half Doesn't Have Any Heating or Cooling
I'm new at HVAC, so I apologize if anything I say isn't correct or if I ask some questions that are extremely basic.
I'm looking for some solutions regarding my current heating and cooling situation. The house is from the 1940's, and has a newer addition. The addition has a Goodman heat pump self contained packaged unit, connected to natural gas, and is 3 ton, 69,000 BTU (according to my Google searches). The old part of the house has duct work underneath, and has an old heater that is not in use connected to it. The old part of the house is 500 - 1,000 square feet, and the whole house is 1,900 - 2,000 square feet. I was told the duct work would be difficult to connect from the Goodman heat pump because there are walls that they would need to go through. I was also told that the duct work under the old part of the house would need to be replaced because it is old and can't handle the 3 ton unit.
I'm looking for the best (and cheapest) way to get heating and cooling on the other side of the house. I prefer to have one unit for the whole house, instead of needing to maintain two units, but it might be too costly to get the Goodman heat pump connected.
I've been looking into the Ductless Mini-Split units from Mitubushi and Fujitsu. Do you think this would be a good option? I've heard they're more efficient that most other options. Is that true?
Please let me know what you think would be the best (and cheapest) option for my situation.