Hello you two
Basically, you should first know what the respective energy certificate requires for the wall surfaces (depending on the house type and location.. or the wishes of the builder). ..after that, you can easily determine which wall thickness, with which material, would fundamentally meet these values.
You can also look around regionally, because not all stones can be delivered to all places in the country at the same price.
Also basically, the heavier the stone.. the more sound insulation it provides (although the question arises how high this would actually have to be and why?), which at the same time would be a disadvantage for thermal insulation.
For a purely load-bearing masonry, a 5 cm thick external insulation will of course never be sufficient today.... you should think in the range of 16-18 cm.
Most suppliers have the appropriate stones in their range to meet the current requirements for thermal protection. Some differ, however, in the variety of products or their shapes and supplementary stones. As long as the mason has a good stone saw at the construction site, the latter characteristic is no longer so decisive.
There are not so many material products.. suppliers/companies and brand names are more common. The most common products are probably aerated bricks (e.g. Poroton/Unipor...), aerated concrete (e.g. Ytong, Hebel..), pumice (e.g. Klimaleichtblock>KLB<, Iso-Bims, Pumix..) or the Liapor products... which are made from expanded clay pellets.
Ultimately, it is also a question of how and with what the local construction companies like to build.. what they know and therefore recommend.. There is usually no point in convincing the selected contractor of a product unfamiliar to him..
My tip: Start with the planning first.. the rest (possibly regarding the budget) usually follows by itself.