ᐅ Floor plan designs for a single-family house on a 640 m² plot with a low eaves height

Good morning!

My girlfriend and I have reserved a plot of land in between other properties, which is being sold privately through a real estate agent, and we already had an initial meeting with an architect. A second meeting with another architect is scheduled for tomorrow. During the first meeting, our needs and wishes were recorded, and at the end, a rather steep price was given. We reluctantly accepted it for the time being and then silently drove home for 30 minutes. We continued researching construction costs and found out that—no matter how you look at it—building significantly cheaper is hardly possible without compromises.

Since then, my mind has been spinning about what the house’s floor plan on the plot could even look like. My girlfriend is dreaming of two full floors and is looking at nice floor plans on Instagram. That is not practical at all in my opinion because a solution deviating from the "standard" is needed to meet our requirements. So these are daydreams that are likely to burst soon. Arguments and conflict are inevitable. I’m trying to prevent that by reading up and educating myself.

I hope for honest assessments, advice, and perhaps some links to helpful threads.

Questionnaire about Your Floor Plan

Zoning plan / restrictions
Plot size: approximately 640 m² (7,000 sq ft)
Slope: yes
Site occupancy index (floor area ratio): 0.4
Floor space index (FSI): 0.7
Setback from property boundary: 3 m (10 feet)
Number of parking spaces: 2
Number of floors: 1
Roof type: gable roof (24–30° pitch)
Orientation: ridge parallel to street
Eaves height on valley side: 3 m (10 feet)
Eaves height on hillside side: 6 m (20 feet)

I will attach the zoning plan including the section to locate the plot, as well as aerial photos later.

Homeowners’ Requirements
Living space: 160–180 m² (1,700–1,940 sq ft)
Basement and floors: maximize floor space index, basement with double garage and office on hillside side
2 (4) persons: ages 32 and 30, 2 children planned
Room needs on ground floor: cloakroom, guest toilet, open living-dining area, additional room (playroom, office for family use, guest room)
Room needs on upper floor: 2 children’s bedrooms with bathroom for children, 1 master bedroom with dressing room and private bathroom
Office: family use on ground floor, home office in basement
Guests overnight per year: 4
Conservative or modern construction: rather conservative style
Open kitchen with island: yes
Number of dining seats: 6–8
Fireplace: yes
Music/speaker wall: no
Balcony: not necessary—if it fits the floor plan, OK, but not essential
Garage, carport: double garage in basement with parking spaces in front
Utility garden, greenhouse: no

House Design

So far, we’ve considered pushing the basement forward so that a terrace could be extended like a kind of balcony in front of the house at this offset. We enjoy the evening sun. Otherwise, I’m holding back ideas and waiting to see what the architect will answer tomorrow to the questions that have come up during the planning process.

What is the most important/fundamental question about the floor plan in 130 characters?

Do you know floor plan designs with similar restrictions (slope, floor space index 0.7, eaves heights 3 m/6 m)? Or any other useful tips? The zoning plan is from 1978—can we negotiate with the city about these requirements?