The correct procedure is indeed to first consider the size of the house (BGF/BRI), the number of floors, the number of completed residential units, etc., and then look for a suitable plot of land, which is likely not easy in the Cologne surrounding area. Perhaps you could have a look around the Zülpich area.
The house design will then be developed by the architect based on this basic concept within the framework of the building and planning law requirements applicable to the desired plot, which are, for example, set out in a development plan: floor area ratio/plot ratio (utilization of the plot); eave and ridge heights, roof shape, building lines, building boundaries, etc.
If no development plan exists, the admissibility of the building project must be negotiated and agreed upon in a preliminary building application according to §34 of the Building Code with the responsible building authorities. The effort required for a basement, due to geological and hydrological conditions, is clarified by a soil survey, which may not be carried out before the purchase but can possibly be inspected for a realized building project in the neighborhood. As a rule, living spaces should be built above ground; basements are basically just costly storage or technical rooms, which can be constructed more cost-effectively elsewhere if the plot conditions allow.
The mentioned cost framework is realistic but is decisively defined by the house design (concept, construction, building services) and your equipment wishes. Here too, the architect can adjust many "control points" to achieve an optimal result within a defined cost framework.