What is feasible on the existing property and budget

You build such a house with an architect. They don't put it up for 500k.

Just briefly about your sketch:
You don't build up the south side with a garage, unless it is at basement level, then you can build a nice terrace on top – but you can't see where the driveway is.
Half a million is enough.
Hire an architect, hillside plots have a lot of potential, but they can also be ruined beautifully.

The garage in that position is of course intended at basement/basement level. The driveway is on the right (southeast). The driveway would be possible over the entire 25 m. The upper street level is approximately 209.5 and the lowest at 207.5, while the reference height for the house is 210.5.

We are unfortunately a bit afraid of a freelance architect, as nearly all acquaintances were far from the architect’s cost framework or the plans were more cookie-cutter than off-the-shelf.
But if the further offers from the construction companies are just as sobering as the first, we will probably have to take the architect route.

Then calculate backwards first:
500k
- 20k kitchen and some small stuff
- 25k earthworks (naturally more expensive due to the slope)
- 30k incidental building costs
- 25k double garage
- 20k carport/entrance canopy
- 30k outdoor facilities (naturally more expensive due to the slope)
____________________
350k

at 2000 EUR/sqm you can afford about 170 sqm.

The carport may be built later and taken out of the budget.
We are still calculating with one income; once the second is secure again, it should be no problem.
However, our cost breakdown is easily 5k more expensive in every point. That leaves only money for a tent.

I also don’t quite understand your reasoning about basement/ground floor/upper floor.
So you want to build 3 stories?
The slope rises, right? I would plan a basement with entrance area, kids’ room, dining area, bathroom, and utility room in the slope. On the upper floor then kitchen/living/dining + office + storage + guest bathroom.
So only 2 floors. Or am I misunderstanding your planning?

Sorry for the confusion. Yes, 3 stories are planned. But we have also already considered your layout with 2 floors (i.e. sleeping in the basement and living on the ground floor and no upper floor). I can’t quite come to terms with that yet. The idea of living in a “hole” doesn’t appeal to me (although admittedly I lived in a hole for 20 years and did not perceive it that way). Besides, a garden access would then be possible only on the northwest side. The southwest side would not be covered for the basement... The question remains where the garage would go then?

In our requests for offers, we originally also asked to push the garage under the house. That always turned out to be more expensive, because the footprint of the house would increase, thermal separation would then be more difficult, and you would also have to somehow catch the slope on the side of the house + create a level surface for a terrace in the garden.

That is exactly what I had already heard here in the forum.

I can't make sense of the elevation data at all
Otherwise, it will be that one moves too much within the layman's standard framework and thus doesn't consider that standard rooms can also be in the basement...

The gray lines are the contour lines. 209 runs across. Top left is the gray 210, and bottom right 208. The reference heights around them are those of the neighboring properties.

My parents' house has already moved out of the framework, but sleeping in the basement is not my first choice, especially since here it would block the chance for the large step-free accessible garden. That's the case at my parents' place. And a nice terrace with a garden doesn't help me sleep. The only really charming thing about the solution, as a future dog owner, is that you just have to open the terrace door if the dog suddenly has digestive problems at night .

Photos of the property with details of the access way and development would be helpful.

The street is on the right (sorry, forgot to mention) and access ways are allowed across the entire street width. On all other sides we have neighbors.

There are no photos since so far only meadow is visible. Development only starts mid-year.

Unfortunately, we are somewhat afraid of the independent architect, since almost all acquaintances were far from the architect's budget or the plans were even more cookie-cutter than the ready-made ones. But if the further offers from the construction companies are as sobering as the first one, we will probably have to take the architect route.

Please give up hope that the architect will be much cheaper. Even then, you need companies or craftsmen who want to be paid. What you do get, however, is an individual house tailored to your wishes/needs.

If you already have an offer. What is he asking for?

The house is located on average at the contour line 209, the garage on average at 208.5 and thus not at a suitable height for roof terrace use nor set back below the windows on the south side - thus I see the planning as needing revision.

The reference height of the plot is 210.5 (compared to the 209 contour line that runs through the house). What is one person's joy (favorable for the knee wall height) is another's sorrow (the basement's view height out of the terrain regarding the critical point of a full story is unfortunately measured by the actual (original) terrain, not by the reference height).

Raising the house close to the reference height reduces the possibilities for the knee wall and will elevate the basement too much; however, this would be necessary for a garage standing an entire level below the ground floor. 1. As sketched, I therefore do not see it arranged as such and 2. I see the floor of the ground floor at around 209 or 209.5 as the most favorable.

3. I see an overall "fox" level of the architect required, which a general contractor draftsman rarely brings along.

Regarding the desired knee wall height >150 I would like to point out that a knee wall is always a dividing line: either only façade windows are below and only roof windows above on the eaves side, or dormer windows must be used. Bent windows on both surfaces have never become a resounding trend for good reason. I therefore advise against such king-size knee walls and see a practical height rather at a finished dimension of 120 (between 100 and 125). A good knee wall completely substitutes a dwarf wall, but not beyond that.