Which floors are suitable for single-family homes? What does the home-building elite recommend?

For children's rooms/bedrooms definitely worth considering.

I especially don't want kids to play on plastic. Every toy is considered for how ecological it is, and then the kids play on cheap plastic...

- Parquet looks great, relatively high quality but certainly not the best choice for children's rooms

Works very well. Just make sure it's not softwood. You can get oak as country house short plank starting at €20. And the manufacturer doesn't matter.

How "difficult" is it actually to glue down parquet yourself? It's strongly recommended for underfloor heating...

Much easier than laying tiles. The glue is pre-mixed, applied to the floor, and then the (usually click) parquet is placed. Afterwards, weigh it down with heavy buckets (at first the unused glue works well for this, later water buckets suffice) – then you can be sure to get a good bond between wood and floor.

I'm mainly concerned about the children's rooms... I think it might be more comfortable for children to play on cork/vinyl flooring than on parquet... But as I said, we ourselves still don't know what we'll do... :(

Save yourself the considerations and all the effort!
1. Different materials
2. Different heights
3. Transitions between the rooms
4. More waste
5. Probably hardly any price difference....

Install everything at once with a "high-quality" covering (= parquet), treat yourself and the children to the joy, and at the same time save yourself the aforementioned disadvantages.

I don't want kids playing with plastic. For every toy, people consider how eco-friendly it is, and then the kids play with cheap plastic...

But my kids won't put the floor in their mouth either (at least I hope so) :D so you naturally pay a bit more attention to such things. But to exclude vinyl as cheap plastic... I also think there are quality differences between manufacturers/products there ;)

I'm mainly concerned about the children's rooms.

By "bedroom" I meant all sleeping rooms..... might also add a play rug if necessary.

My kids also won’t be licking the floor (at least I hope so) :D so of course you pay a bit more attention with such things. But to rule out vinyl as cheap plastic... I also think there are quality differences between manufacturers/products;)

My child regularly licks the floor.
No idea what fascinates her about it so much, but not a speck of dust is safe here.

My child regularly licks the floor.

oh ok yeah then I have to rethink that o_O. I better order 2-3 samples to see what tastes better to mine, in case they ever come around to the taste. :D They are still young, you never know