Heating system for our single-family house!

The gas connection must be in place up to the gas condensing boiler in the end, that should be clear and has to be paid for.

Sounds to me more like the public development and the installation on your property is an additional cost on top

The gas connection to the house must of course be paid for separately. I meant that we have paid for the gas during the public development.

The last meter to the house was only 600 euros here. The heating system was 7000 much cheaper than a pump. And Yvonne already said: A gas boiler is also something for tech dummies. Turn it on, warm, good. No flow temperature, no this and that, no fiddling, it does everything automatically, and that's good. And it is small in the utility room, still leaving plenty of space for shoes, cupboard, cat litter box, etc. K.

Are 300 l enough for us "warm showerers" or will we have no warm water left at the end of the day?

Try searching the relevant search engines for the "Duschrohr" from Wagner Solar.

This is a double-walled wastewater pipe, which is connected to the shower. The warm shower wastewater flows through the pipe along a heat exchanger through which the fresh cold water simultaneously flows towards the hot water storage tank.
In this way, about half of the waste heat is supposed to be recovered. This saves costs on one hand, but also increases the amount of usable water in the storage tank.

On paper, it should actually be possible to operate the condensing boiler in accordance with the Energy Saving Ordinance again using this pipe in combination with a controlled residential ventilation system, thus dispensing with solar thermal energy. The main difficulty is likely to be finding an energy consultant who is able to provide this proof using standard programs (as there is no "checkmark" for this yet).

The part costs about ~550€ for the large version plus installation and is now even subsidized by BAFA (unfortunately only from 6 units, so nothing for a typical single-family home).

With or without the Duschrohr, 300l is more than enough for 4 people. With the Duschrohr, we even went down to 200l and we will soon be five.

I don't want to start a fundamental discussion here about whether an air-water heat pump or gas/solar is better.

If you have no idea about the air-water heat pump and the whole thing, you should take a solid gas heating system.

What I always say – regarding wall construction: take the stone that your builder "knows" – this applies accordingly here, both for the heating "method" and for the choice of manufacturer: better the theoretically or according to tester opinion possibly only second-best offer for the individual case than the very very best one, for which, unfortunately, you would be a "guinea pig" in the sense that the installer hasn’t had much experience with it yet.

[...] A gas boiler is also suitable for technical dummies. Turn it on, warm, good. No flow temperature, no this and that, no fiddling, it does everything automatically, and that's good. And it's small in the utility room, still plenty of space left for shoes, cupboard, cat litter box, etc. K.

Explain. I would say, an air-to-water heat pump can also be set to "auto." Both systems only run truly efficiently when used smartly.

A gas boiler is also something for tech dummies. Turn it on, warm, good. No flow temperature, no this and that, no messing around, it does everything automatically, and that is good.

Incredibly qualified. The underfloor heating thanks you. And with KfW55 and better, you won't get the heat out of the house.