Hello Timo
So you have already received quite a bit of information about the cellar. I want to stay out of further discussions about the cellar now because I am not that familiar with the subject, and I have already given you my opinion.
Regarding the cistern, I can tell you the following. I buried a plastic tank with 4 m³ capacity according to the manufacturer. I once filled it using a non-calibrated water meter and found out that according to the water meter, significantly less than 4000 liters fit in. Unfortunately, I cannot state the exact difference now as I do not remember these values anymore. However, it was a considerable difference. Whether this means that the tank's actual capacity is smaller than stated or the meter did not measure correctly, I cannot say. But it would not surprise me if the manufacturers give the external volume as the tank size rather than the internal volume. But as I said, just a guess.
As mentioned above, this tank is buried. There are flat tanks and deep tanks (I have one of those). Flat tanks are more expensive but do not require such a deep hole. The downside is that you have to expect the remaining water to freeze in winter. Therefore, a tank buried deeper would be better.
I converted an existing property accordingly. This means all roofs as well as the driveway were connected to the tank, and in return, the existing connections to the sewer were deactivated. Specifically, I completely relaid the pipes and left the old ones in place, so to speak: in case the city changes its mind, and wants money again, I can easily rebuild and they can take care of the rainwater themselves.
What I am saying now refers to what applies here according to my knowledge.
When the tank is full, there is the option to channel the excess into the sewer. But that costs fees again.
It can be disposed of via an infiltration trench. For that, I would have needed a permit from the lower water authority, where the question whether it would be approved or not alone would have cost 100 €. Additional costs for the infiltration unit would have come on top.
That was a bit too expensive for me, and also, I would not have known where to bury this infiltration unit anyway, since there are many trees in the garden.
My alternative: using a simple sewage pump to ensure that the water level only reaches a maximum value, and the excess water is pumped into a wastewater pipe which I laid above ground in the garden. I cut some lateral slits in it and can thus, by turning it, adjust more or less where the water would flow out in case of need. Regarding the appearance, it can be more or less well concealed by suitable planting.
Regarding the tank size, have a look under "Rainwater tank calculation" or similar terms; there you can find out which size you probably need. But beware, I found that you can arrive at different results on different sites using the same data. I can only say that my tank was partially emptied by the pump several times in spring 2016, and I could have used this water well in summer. That means, better to install 5 m³ more than 1 m³ too little tank capacity, to put it that way.
I cannot say the exact material costs. But roughly:
Tank 750 €
Pipes, bends, etc. 100 €
Two pumps at 40 € each 80 €
Water level switch 50 €
Drainage channel 250 € (could have taken cheaper ones)
Miscellaneous 100 €
So that is a total of about 1300 €. But all done as DIY.
How it ultimately looks for you, you have to calculate yourself.
Sorry, the text has become a bit long. But I hope I have answered the questions about the cistern as well as possible.