The split AC is divided in two parts - one inside the room and one on the outside, which means that it takes more space than the window and portable ACs. However, if you value the inner space more, the portable AC would be the worst choice as it’s a single but big unit placed on the floor near the window.
Regarding design, probably the inner body of the split AC looks best, considering that it takes less space in the room and is usually mounted high on the wall. However, its outer body is not very pretty, so if you care more about the exterior you should choose the portable AC. It’s the only one from the three types that cannot be seen from the outside of the building.
If you’ve bought a split air conditioner, you should call a professional to install it. As both the inner and the outer body are mounted on the wall it will cost you more than installing window or portable AC. You can install the last two on your own and it will be cheaper. However, you should consider your window type and size before buying a window unit. For the portable air conditioner this doesn’t matter and you could also vent it through a door or the ceiling. Note also that the portable AC could be easily moved from one room to another.
As the split AC’s compressor is outside the room, it’s the most quiet option. The compressor and the evaporator of the Window and Portable ACs are at the same place, which makes them noisier. However, the noise level of the portable AC may vary depending on the model.
The fact that in the split system the cooling unit is separate than the compressor enables manufacturers to make the AC more powerful. The cooling capacity in the window and portable ACs is limited. Consider those differences between the three types of AC to choose the one that works best for you.