ᐅ Single-Family Home – Choosing the House Type and Location

Dear all,
I am currently searching for a plot of land but am not making much progress because the resulting costs can vary greatly, which significantly affects my remaining budget.

I House Type
I would like a single-family house in the Bauhaus style, but with a brick veneer. My wife prefers a “traditional” house with a pitched roof or a half-hipped roof, but she would agree to the Bauhaus style if it does not lead to (significant) additional costs. In my opinion, the Bauhaus style should be more affordable due to its presumably more favorable volume-to-exterior-surface ratio and the flat roof, compared to a similarly equipped traditional house, right?

II Plot and Costs
We currently live in the commuter belt of Hamburg in Schleswig-Holstein and like this area very much, but the connections (transport, shops, schools) are rather poor. If we were to move closer to Hamburg, however, the land prices increase. Here, they are currently around 250 €/sqm (square meter), while closer to Hamburg (depending on the district) they range from 350 €/sqm, 440 €/sqm, up to 550 €/sqm.
Although I am planning with what I consider a generous total budget of about EUR 650K (170K equity), I quickly reach my budget limit given my desired plot size of 800 sqm (700 sqm minimum), especially since I cannot reliably estimate the house costs.
Since plots here are highly sought after, some are reserved within just 2-3 days, and binding confirmation— including bank financing approval—may be required within 14 days. As I cannot plan a house including costs and zoning restrictions within that timeframe, I want to clarify as many questions as possible in advance.
I would therefore appreciate your feedback on the overall project and expected costs so I can refine my plot search accordingly.

III Size and Equipment
The house should include the following rooms. How do you assess these sizes? Am I missing anything?
3 children’s rooms (each 18 sqm) 54
Bedroom 20
Kitchen 15? (separate room, not open-plan)
Guest room 18
Library 25
Dining room 20
Study 16 (maybe in the basement)
Living room 40
Total living area 193
Usable area (25% of living area) 48
Footprint 240

Are the bathrooms (2-3) included in the usable area, or do I need to add extra space for these?
Is the assumption of the usable area realistic?

The house should have a full basement, a central ventilation system with heat recovery, underfloor heating, and a stove. A garage would be nice but is not a priority.
An architect once gave me a rough figure of EUR 400K (including additional construction costs) for these requirements, but without the basement, though including the garage and floor coverings at 30 €/sqm. This matches the often-mentioned 2,000 €/sqm price, but what level of finish can I expect for this?
Ultimately: If you believe that the house described above in “really nice” condition is only available for, say, > 450K + extras, I would limit myself to the “cheaper” plots and perhaps buy a larger one there. If the house can be realized in “really nice” condition for 350K-400K, I would consider financing up to an additional 100K and looking for a better-connected plot.
Finally, assuming the restriction that the first floor may be a maximum of 60% of the ground floor’s living area, how large would the plot need to be in your experience to allow sufficient maximum buildable area? (I understand that zoning regulations vary greatly...)
Thank you very much
Sullivan