Good mini-splits should handle your place both for heating and cooling. The big thing is to figure out what size you really need. The choice can get a little complicated depending on the floorplan of the house...the more open it is, the easier and less expensive it will be since you need fewer heads or units. The good ones provide heat at much lower temperatures than the older ones. They would free up space in the house as well. Read a few similar threads here and you'll get enough info to start to evaluate what's going to be required.