Heating single-family house, underfloor heating conversion, insulation, gas boiler defective

Can you give me a tip on what you would personally choose.

General recommendations are hardly possible, since, as already mentioned, the actual demand for heating and hot water is not known. For any type of heat pump, however, the heating surfaces must be designed so that a system flow temperature <= 35°C is possible. This means correspondingly large heating surfaces, small spacing of pipes, many heating circuits depending on the room heating load. With high room heating loads, one often reaches limits in existing buildings. Additional domestic hot water is not uncommon, especially in bathrooms! It should also be considered that a paid natural gas connection is already available!!! With natural gas, cooking can also be done very cheaply ;-) Compared to standard radiator systems, an additional 15...35% energy savings can be achieved with efficient use of heating surfaces (special design/dimensioning), especially since heating ad libitum is possible, which is hardly feasible with underfloor heating. Tending to, without knowledge of the individual boundary conditions and therefore subject to reservation, I would tend towards gas condensing boilers (large modulation range) with radiators. Best regards

How do you find convector heaters, I personally have no experience with them, but have heard from acquaintances that they cause only low costs both in purchase and operation.

...have heard from acquaintances that they cause only little cost both in purchase and in operation.

Convectors "rely" on high supply temperatures. Especially these are to be avoided with modern heating systems for reasons of energy efficiency.

Best regards.

Good, I did not know that.
thank you

So if I decide on a gas condensing boiler, which one should I choose? It must also heat the hot water for me, either via a storage tank or directly with the gas instantaneous water heater. Which manufacturers are recommended .....?

So if I decide on a gas condensing boiler / heater, which one should I choose?

That cannot be said like this; first, the heating load must be calculated. Affordable are those with as large a modulation range as possible. So with indirectly heated storage.
If devices are equivalent (in price), preference should be given to those whose control allows variable power adjustment of the heating circuit pump. For this function, there are different manufacturer designations, e.g., "Eco," "Eco +," or similar. Everyone just calls their horse differently ;-)

Best regards