Difficult plot due to hillside location

Should the basement be developed or become a utility cellar?
If you look at the hillside location, you could also consider building the garage on the east side, a bit further back at ground level (so recessed compared to the house - maybe at basement level) and thus have both the southwest side of the house free and the view to the southeast towards the mountains.
However, it will be significantly more complex regarding wastewater and earthworks!

Without seeing the site and surroundings and without knowing the lifestyle preferences, one can only guess or base considerations solely on possible construction costs. That does not help.

The basement consideration should be based on lifestyle needs. On a slope, a basement is often usable with natural light on one side. That is an advantage. The opportunity costs of building without a basement are higher on a slope, as the extra cost for a basement on a slope is generally lower than for a house on flat land. This makes the basement comparatively inexpensive. However, the basement usually still causes additional costs.

I like the idea of a garage under the house - but for cost reasons, we did not realize it ourselves with our site and house.

https://www.hausbau-forum.de/threads/grundrissplanung-unbedingt-vor-Beitrag-Erstellung-lesen.11714/ If you don't know which rooms you need, how are you supposed to give recommendations for the house location?????? Why a 9x12m house? Is the slope between the respective elevation points even? Are the elevation points then set at the actual depth where they occur? So -2.33m at about 17 m plot depth? My first idea would be: create an entrance in the south/west, and then the ground floor at street level, basement underneath towards the west in the back, east/north with windows for the children's and parents' sleeping area. On the ground floor, dining/cooking towards east/south, living area rather east. Then a terrace on the south, which transitions for the basement in a kind of shelter.