If your basement is mostly underground and you have one or two small windows then installing a mini split is over kill in my opinion. The basement requires no cooling in the summer. In the winter the heating load is much smaller than you think. This is due to the fact the basement is below grade, plus the installation you will be adding, and the first floor above is heated.

How cold does the basement get in the winter, and how warm does it get in the summer? Adding some registers and a return is likely to be sufficient for most winter days. You could an add an electric baseboard heater as a supplement for cold days.

We have a similar above ground apartment with living/dining/kitchen area, short hall, bath and small bedroom. There is a mini-split in the large area, plus supplemental electric heat in the bath and bedroom. The mini-split does the heavy lifting all year round for heating and cooling. In a basement I would be surprised if you needed more.

we have a finished basement (7' ceilings). It's about 1600 sf. We put a single zone mini split down there. Heats everything, was probably overkill but works well. The basement is separated into 4 rooms (mudroom/laundry room, office/storage, rec room/kitchenette/bar, and a full bathroom). As long as the doors are open between the rooms, the mini split keeps the space comfortable. Before we installed it there were some wall mounted blower heaters.