Hello,
...The house is being built in an area where no gas connection is available, so at most one could rent gas tanks. We definitely do not want oil.
With gas or equivalent conventional heat generators, a solar thermal system, which is often uneconomical in single-family houses, usually has to be purchased compulsorily. The cheaper way here is better insulation => 15% rule. Liquid gas is usually an expensive option.
With conventional heat generators based on combustion, the consumption is always higher than the demand, so the achievable annual efficiency plays an important role.
...Of course, we would prefer a heat pump.
Here the consumption is lower than the demand. Therefore, from an economic point of view, the insulation requirements are less demanding.
However, here the necessities of careful and exact planning of the entire system are particularly high. If this is neglected, one quickly ends up with a money pit and the theoretically high efficiency cannot actually be utilized. A defect from which currently quite a few, especially GU/GÜ systems, suffer.
...Can you recommend one? Alternative energy sources are also welcome.
For this, the specific conditions of the construction project would have to be known; anything else would be a look into a very murky crystal ball.
In principle, air heat pumps, brine heat pumps, and less frequently groundwater heat pumps come into question.
First, have the actual demand (power, energy) for heating and hot water calculated. In connection with the respective solution, this results in the actual consumption, with which an investment can then be evaluated.
Best regards