So, then I'll get back in touch.
First of all, thanks for the answers. I'm already aware that the 20,000 is rather unrealistic.
What would you set as the absolute minimum for pure material costs?
The excavation for the basement... well, you have to get some machine help for that... That is also own work, but for day 2 you just have to rent an excavator. Although I was actually told that basements were dug that way back in the post-war period...
On the topic of electricity & co:
In general, we want to live independently and self-sufficiently (keyword self-sufficiency). Nevertheless, we of course don't want to give up the "luxury" of modern life (keyword sewage & internet). Also because of the children (bullying). So all these mandatory connections have to be made (and were not even included in the 20,000).
On the topic of can or want:
I'd say both. At the moment we are in the saving phase anyway. We want to avoid a loan anyway. So purely equity.
Of course, I've also thought about buying one of the old houses in the East. That would still be an idea. The problem with that: The old shacks naturally like to hide surprises (water damage, mold, dilapidated ceilings... I think you know what I mean) and a total renovation would be nice as a hobby project, but it also has to be manageable in terms of time.
With a new build I know: Okay, that takes 3-6 years with own work (or however long). With an old building renovation I might put in 2-3 years of free time, move in and then realize that something is wrong that basically makes the object uninhabitable. Especially since with old buildings a new heating system usually has to be installed anyway due to legislation...
Speaking of heating. How is that actually? They all have to be replaced at the moment. What if you throw out the oil boiler and then install a fireplace (of course approved by the chimney sweep). Is that okay or does the legislator have some complaint about that too?