Split is the way to go.

A "heat pump" is the entire system, not just the inside part. They work by pumping heat from one place to another. Typically air cons pump heat from inside to out, but since the components inside and out are about the same, many systems can run in reverse, pumping heat from outside to in. This is way more efficient than a resistive heater.

The cool thing about split systems is you can have heads in all the rooms, and use them only when you need them.