First steps of a young four-person family

370€ including incidental construction costs would be very difficult in the Cologne/Bonn area, from my limited experience. Berlin is, I believe, rather expensive as well...

Unfortunately, we do not have any contact person at all, neither among friends nor family, who owns a home and can support us with initial questions. Therefore, here is my attempt to get some input from you.

Welcome!
Although you have come to the right place and there are already some posts, judging by the way your posts sound, you are still VERY much at the beginning in terms of your knowledge. That’s not bad, we’ve all been there once (unless you already work professionally in the construction industry).
My only advice is to first invest dozens of hours in searching through and reading here (and also the rest of the WorldWideWeb including YT) and to read, read, read/listen.

Good luck.

I can only advise to first invest dozens of hours in searching here (and also elsewhere on the WorldWideWeb including YT) and reading, reading, reading/listening.

or you use this time to further your professional education, thereby activating more salary and continue to live comfortably renting.

Developer property (?) Here it would then be a kind of complete package, meaning house and land? [...] How do I come across the mentioned developer properties? And what exactly is this about?

Developers are, in a way, commercial builders. They develop a plot of land by building a house on it and then sell the fully developed property. Practically like a demonstration car with zero kilometers, only as a house. It was actually common that the developer built a house, based on their experience likely to sell quickly, without knowing the specific buyer. In recent years this has increasingly changed: today a buyer is more often found first and then building begins. This allows the buyer to incorporate more wishes, at least in the case of a single-family house or a semi-detached house. For row houses, however, the design framework customary in the past has remained, i.e. the options are limited to, for example, kitchen integrated or separated from the living room by a partition wall or similar. An advantage of the formerly more common procedure was that the house was at least substantially constructed in terms of the shell while today you often cannot visit it but only see it as a drawn concept. Today the depth of design is higher, the buyer "plans" significantly along. As a result, buyers increasingly feel like builders themselves and confuse in discussions the terms "general contractor" (builds, possibly "turnkey," on your plot of land) and "developer" (always builds turnkey, on their plot of land). Developer properties are easy to find since developers, after all, advertise them. Often the properties are offered as existing properties and are only recognizable by notes such as "construction start summer 2020." Unfortunately, many developer properties are also offered like plots of land, which you can only acquire by signing a building contract with the seller. There is no shortage of developers of all levels of seriousness in big cities and metropolitan areas. Even though this rule is not reliable, in my opinion the better developers are often also active as general contractors besides that. They often cooperate with regional banks, where they can be found in real estate brochures. In larger area developments they regularly take part, for example when barracks, industrial brownfields, or freight yard sites are repurposed. Basically, they are hardly avoidable; you practically stumble over them. Look out in the newspaper for half-page drawn images that look like baking pans full of row and semi-detached houses surrounded by lots of greenery and happy cyborgs.

I just completed a house renovation (3 years ago) and friends are renovating the neighboring house for themselves. What I notice (design is my profession) is that "people" often have certain criteria in mind "without which it won't work". But these are usually what the neighbors have. If you free yourself from these "specifications", you can save a lot of money. You can also live very well with "less" and not everything that is "normal" here in Germany is necessary.

What I notice (design is my profession) is that "people" often have certain criteria in mind "without which they can't do." But that is almost always what the neighbors have. If you free yourself from these "requirements," you can save a lot of money.

That's why part of the success formula of developer housing estates (just kidding!) is that the neighboring houses resemble each other like one pristine white shoebox to another.