What is feasible on the existing property and budget

Hello everyone,
somehow I am stuck in a chaos of planning thoughts and am hoping for a few tips from you on the approach to planning and/or ideas for implementation...

In particular, a cost estimate would probably help me regarding the basement design. Or how many square meters of house we can afford. Can we save if we plan the garage in the basement instead of a living basement and enlarge the house footprint for guest rooms/office and utility room?
What is the most cost-effective way to achieve my desired ground-level access from the ground floor (living/dining/kitchen) to the large terrace and garden? There should be enough space to at least partially compensate for an embankment with a slope?
Are there ideas for the placement of the garage? I can't really imagine the slope properly.
We have a total of €500,000 available (plot already owned). It should somehow be feasible with this budget as a family to build a house (not just standard equipped) with more than 130 sqm plus basement, garage, and outdoor area in Baden-Württemberg, right??

Development plan/restrictions
Plot size: approx. 769 sqm (development and final measurement will still take place)
Slope: yes, 2 or 3 meters slope
Floor area ratio: 0.4 (max. 0.6)
Floor space index: -
Building window, building line, and boundary: 2.5 m distance from boundary
Edge construction: garages if connected to the main building; 1 m distance on street side
Number of parking spaces: 2
Number of floors: -
Roof shape: SD, vSD, WD 30 - 40°: max. ridge height = 8.0 m
ZD, gD 10 – 25°: max. ridge height = 8.0 m
FD 0 -5°: max. eaves height = 6.8 m
Style: -
Orientation: parallel to the street or rotated 90°, see plan
Maximum heights/limits: height applies from reference height (highest point on our plot); max. ridge height 8 m (with FD max. eaves height 6.8 m)
further specifications:

Requirements of the builders:
Style: modern, but above all practicality outside before appearance!
Roof shape: doesn’t matter, just no knee walls below 1.50 m
Building type: doesn’t matter
Basement, floors: first idea living basement with owner-occupied granny flat; alternatively living basement with guest room/office or utility basement with integrated garage?? this is exactly where part of the planning problem begins
Number of people, age: 36 and 38 + 1.5
Space requirements on GF, upper floor:
GF: (on one level with garden access or large terrace) 50 sqm for open living/dining/kitchen; the rest results from wishes such as WC or shower bathroom, entrance area/wardrobe as a dirt lock, i.e. walking area of the stairway and WC not in the dirt brought in at the front door; small office/alternate guest room, possibly a closet for vacuum cleaner, broom, etc.
Upper floor: bathroom with double washbasin, duo tub (180x80), bright floor-tiled shower 1x1.2 with glass door; 1 large (>15 sqm) and 1 smaller (approx. 12-15 sqm) children’s room; bedroom, dressing room (accessible from the hallway), small hallway (no waste of space for a large hallway, rather bigger rooms), possibly utility room for washing machine, dryer, ironing, and drying rack
Office: family use or home office?: both; both adults home office about 1 day per week.
Guests per year: around every 2 months 1-2 guests, possibly increasing due to childcare
Open or closed architecture: open!
Conservative or modern construction: rather modern, many floor-to-ceiling windows, light light light...
Open kitchen, kitchen island: open kitchen!!! Preferably with island (possibly not enough space); important: sink and work surface not facing the wall and not facing away from the living-dining area!! (wish side-by-side, tall oven)
Number of dining places: 4-6 (more than 6 only with extendable table and chairs brought in)
Fireplace: possibly preparation
Music/stereo wall: no
Balcony, roof terrace: due to slope garage roof on basement level as roof terrace for GF
Garage, carport: double – preferably large garage. 2 Sunday vehicles MUST fit in the garage with tools and some space for tinkering. For 1 everyday vehicle garage or carport (comfortable getting in/out and short, stair-light access to the house entrance, preferably covered). 1 more everyday vehicle somewhere (e.g., parking space in front of garage or so)
Kitchen garden, greenhouse: no
Other wishes/special features/daily routine, also reasons why this or that should not be:
ground-level access from kitchen/dining/living to garden is a must, alternatively large roof terrace leading to garden!
Wishes for the future: option to build a pool; retrofitting smart home

House design
From whom is the planning:
-planner from a construction company
-architect
-do-it-yourself
What do you like especially? Why?
What do you not like? Why?
Price estimate according to architect/planner:
Personal price limit for the house, including equipment: €500,000 for the house including everything, i.e. also including earthworks, kitchen, outdoor area (possibly in parts) and double garage
Preferred heating technology: Gas not connected, therefore air heat pump, preferably with photovoltaics

If you have to renounce something, which details/extras
-can you renounce: for now the 3rd garage or carport for the everyday vehicle or an oversized double/large garage if the planning allows later realization; granny flat, living basement (if office on ground floor and utility room on upper floor), basement (if the slope allows and house footprint becomes larger), stair-light access to the house, fireplace
-can you not renounce: 50 sqm for living/dining/kitchen, open living, dirt lock, floor-to-ceiling windows, electric shutters,

Just briefly about your sketch: The south side is not built up 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. Get an architect, hillside properties have a lot of potential, but you can also ruin it nicely.

Just a quick note about your sketch: You don't build on the south side with a garage, unless it's 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. Get yourself an architect; hillside plots have a lot of potential, but you can also really mess it up.

Have you ever questioned why the OP is asking this budget question? Everything finished with a 3m slope and not a run-of-the-mill design for 500k€? We have the same conditions except for the bathroom fittings and the garage, and when everything is finished – really everything (except furniture) – I'm at 480-500k€, just for the house. However, I am already building and that in BY and not in BW. So I don't see his 500k€ as a pain threshold set in stone.

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

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

That should be enough for 3-4 people.
But you have to say that your wishes are already cost drivers. Just the double garage + carport/entrance canopy will cost quite a bit. Photovoltaics and others probably won’t be included at first.

I also don’t quite understand your considerations 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, children’s 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 stories. Or am I misunderstanding your planning?

We are building similarly on a slope. The terrace for us will also be above the double garage. When we requested quotes, we originally asked to push the garage under the house. That actually always came out more expensive, as that would increase the base area of the house, somehow make thermal separation more difficult, and you would also have to somehow retain the slope on the side of the house + create a level area for a terrace in the garden.

Have you ever asked yourself why the OP is asking this question about the budget? Everything fixed and finished with a 3m slope and not a standard model for 500k€?

Of course, you can also spend more, but if you set 500k as the limit, it is definitely feasible as a non-standard house.

I can’t deal with the height specifications at all Otherwise, it will be that one moves too much within the layman standard corset and thus does not consider that standard rooms can also be in the basement...

How can I most cost-effectively achieve my desired ground-level access to the large terrace and garden from the ground floor (living/dining/kitchen)?

Then, of course, the full desired package comes into play

first idea: living basement with owner-occupied granny flat; alternatively living basement with guest room/office or utility basement with integrated garage?? This is exactly where part of the planning problem already begins

Double—preferably a large garage. 2 Sunday vehicles MUST fit in the garage with tools and some space for tinkering. For 1 everyday vehicle, garage or carport (comfortable getting in/out and short, low-stairs paths to the house entrance, preferably under a roof). 1 other everyday vehicle somewhere (e.g., parking space in front of the garage or so)

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