I have an interesting situation where I am in a studio that is approximately 300 sq. ft., and should require ~9,000 BTU/h (3/4 ton) heating/cooling capacity. There are three rooms--A bedroom (~11x8), a living room/kitchen (~13x13), and a bathroom (~7x4). No current HVAC system currently exists, and I only really have access to the ceiling. Currently no insulation exists, but I plan on adding some (>R15 in walls, >R40 in attic). Also, this is in California, where I expect the normal temperatures to be between 0°C and 30°C.
My current problem is in finding a solution that provides heating and cooling to all three rooms. I was hoping to use a mini-split system, but I need it to operate on 120V and it would need to have a horizontally ducted interior unit to provide for all three rooms. Unfortunately, the only systems with horizontally ducted interior units seem to run on 208/240V and they seem to cost twice as much as an equivalent wall-mounted interior unit system.
An alternative I considered was putting in a system with a wall mounted interior unit and adding some duct work to actively ventilate the other two rooms. I'm not quite sure how to tie this into the thermostat for the mini-split, though.
Lastly, I looked at central heat pumps, but those all seem to be excessively sized for my conditions and would require duct work be added, which may not be a problem. On the side of the studio where the external unit would be, there is a closet that shares a wall with each of the three rooms, so a ducted solution could be placed inside the closet, or just above it, minimizing the duct work needed.
I'm really wondering what type of system would be best for my studio. I am looking to spend