ᐅ What is feasible on the existing plot and within the budget

Hello everyone,
somehow I’m stuck in a planning chaos and hope to get a few tips from you regarding the planning approach and/or ideas for implementation…

In particular, a cost estimate would probably help me with regard to the basement design. Or how many square meters of house we can afford. Can we save money if, instead of a living basement, we plan the garage in the basement and enlarge the house footprint to accommodate a guest room/office and utility room?
What is the most cost-effective way to achieve my desired level access to the large terrace and garden from the ground floor (living/dining/kitchen)? There should be enough space to at least partially accommodate an embankment with a slope.
Any ideas for the placement of the garage? I especially can’t quite visualize the slope.
We still have a total budget of 500,000 € (land already owned). It has to be somehow feasible with this budget to build a family 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 (access and final measurement still pending)
Slope: yes, 2 or 3 meters (6.5 or 10 feet) gradient
Floor area ratio: 0.4 (max. 0.6)
Floor space index: -
Building window, building line and boundary: 2.5 m (8 ft) setback from boundary
Edge development: garages, if connected to the main building; street-side 1 m (3 ft) distance
Number of parking spaces: 2
Number of floors: -
Roof shape: single-pitched (SD), half-hipped (vSD), gabled roof (WD) 30 - 40°: max ridge height 8.0 m (26 ft)
dormer roof (ZD), gable dormer (gD) 10 – 25°: max ridge height 8.0 m (26 ft)
flat roof (FD) 0 -5°: max parapet height 6.8 m (22 ft)
Architectural style: -
Orientation: parallel to the street or rotated 90°, see plan
Maximum heights/limits: height measured from reference height (highest point on our plot); max ridge height 8 m (26 ft) (for flat roof max parapet height 6.8 m (22 ft))
Additional requirements:

Client requirements:
Style: modern, but practicality on the outside more important than aesthetics!
Roof type: doesn’t matter, just no knee wall under 1.50 m (5 ft)
Building type: any
Basement, floors: initial idea is a living basement with a self-contained apartment; alternatively living basement with guest room/office or utility basement with integrated garage?? This is already part of the planning problem
Number of people, age: 36 and 38 + 1.5 years
Space requirements on ground floor and upper floor:
GF: (level access with garden connection or large terrace) 50 sqm (540 sqft) for open living/dining/kitchen; the rest depends on wishes such as guest toilet or shower bathroom, entrance area/wardrobe as a mudroom to avoid dirt being brought into the house, circulation area for stairs and guest toilet not in the dirty area right at the front door; small office/spare guest room, possibly a pantry for vacuum cleaner, broom, etc.
UF: bathroom with double vanity, bathtub for two (180 x 80 cm (71 x 31 inches)), bright floor-tiled shower 1 x 1.2 m (3 x 4 ft) with glass door; one large (>15 sqm (160 sqft)) and one smaller (about 12-15 sqm (130-160 sqft)) children’s bedrooms; master bedroom, walk-in closet (accessible from the corridor), small hallway (no wasted space for large hallway, prefer bigger rooms), possibly utility room for washing machine, dryer, ironing and drying rack
Office: Family use or home office?: both; both adults work about one day a week from home.
Overnight guests per year: around 1-2 guests every 2 months, 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 an island (possibly not enough space); important: sink and work surface not against a wall and not facing away from living-dining area!! (Wish side-by-side fridge, tall oven)
Number of dining seats: 4-6 (more than 6 only with extendable table and chairs to be fetched)
Fireplace: possibly preparation
Music/speaker wall: no
Balcony, roof terrace: because of the slope garage roof on basement level as roof terrace for the ground floor
Garage, carport: double—preferably large garage. Two cars used only on weekends MUST fit in garage with some space for tools and repairs. For one daily-use car garage or carport (convenient getting in/out and short, low-stair access paths to house entrance, preferably under cover). One more daily car somewhere else (e.g. parking space in front of garage or similar)
Utility garden, greenhouse: no
Other wishes/special features/daily routine, also reasons why this or that should or should not be:
level access from kitchen/dining/living to garden is a must, alternatively large roof terrace leading to garden!
Future wishes: possibility to add a pool; smart home retrofit

House design
Designed by:
-builder’s planner
-architect
-do-it-yourself
What do you like especially? Why?
What do you dislike? Why?
Price estimate by architect/planner:
Personal price limit for the house including equipment: 500,000 € for house including everything, also earthworks, kitchen, outdoor area (possibly in installments) and double garage
Preferred heating technology: gas not connected, therefore air-source heat pump, preferably with photovoltaics

If you had to forego some details/extensions
-You could live without: for now the third garage or carport for daily vehicle or oversized double/large garage, if planning allows later realization; self-contained apartment, living basement (if office on ground floor and utility room upstairs), basement (if slope allows and house footprint increases), stair-low access to the house, fireplace
-You cannot do without: 50 sqm open living/dining/kitchen, open living, mudroom, floor-to-ceiling windows, electric shutters,