Which heating system should one choose for a new building?

Those would be good conditions for a ground source heat pump with surface/trench collector. Especially if you can do some of the work yourself, you will come out ahead thanks to the subsidy (BAFA €4000). But a heat pump does not fit with a fireplace with heating support (the latter, in my opinion, fits nothing except the seller’s wallet and the user’s sentimentality)

I don't think much of that because my garden is only aligned according to no larger trees, shrubs, possibly a pool, etc., everything has to be aligned accordingly..... best regards

Yes, exactly that is not correct. My acquaintance laid the collector in the trench at a one-meter boundary distance. It is also so deep that you can safely plant over it. However, the pool cannot be above it. But you could heat the pool via the heat pump and do so cost-neutrally in summer with photovoltaics.

Please do not immediately rule everything out without informing yourself.

Cost-neutral is also not true in summer. The system has to be paid for, the consumed electricity is not paid for by the grid operator, and the VAT and the free supply to the heat pump must also be taxed.

All in all, photovoltaic electricity costs exactly the same as from the grid. (plus or minus a few cents).

That is new to me, could you possibly explain that via PM?

The trench collector is so far little known in Germany.

There is a local provider here for whom this is practically standard (whatever exactly is behind it). In my opinion, it is especially worthwhile if you construct the trench yourself.

We also installed a surface collector ourselves. We needed about 350m² of area and laid 650m of pipe. The effort was about 8 hours with 4 people (excavator driver, my future wife + her brother and me) spread over 2 days. I estimate the cost at a maximum of 1000 euros! The shaft where the brine pipes converge and the distributor is located was somewhat more complex. For this we cast a small base slab (2m*1.4m), set shuttering blocks and filled it with concrete, then cast a ceiling with in-situ concrete again. The effort was certainly 30 hours, and I estimate the material costs at 600€). It can also be done simpler or smaller. But since we built the entire heating system ourselves (family member = specialist), the shaft should at least allow comfortable work. The brine pipes are extremely stubborn, and connecting them to the distributor in a tight space is even less fun. In the circle of acquaintances there are other surface collectors, where gardens or trees have also been planted on them. You just have to make sure not to build over them.