Hello,
here is a suggestion on how it could be done based on the drawing.
Guest = 2 connections as double socket with modular jack
Living / Dining = 4 connections as double socket with modular jack
Hallway = 1 connection as ceiling outlet for access point, power supply via POE adapter. Connection using modular jack or field-configurable plug
Gallery = same as hallway
Child 1 = 2 connections as double socket with modular jack
Child 2 = same as child 1
Sleeping = same as child 1
What might also be interesting:
Network connection for video door system
Network connection for doorbell
Network connection in kitchen
Network connections outside
Network connections for cameras
Suggestion for improvement:
I would rather place the access point in the hallway centrally between living/dining area and kitchen. You spend more time there than in the hallway and the hallway is supplied via the access point in the upper floor gallery.
According to the drawing, 14 cables would lead into the utility room.
An additional slot on the switch is needed for the router (e.g. Fritzbox or Speedport).
How old are your children / do they already need network connections?
With full occupancy, you would need at least 15 connections, so the next common switch size would be a 16-port switch.
Are there other devices you would like to integrate into the network via cable? Examples would be a printer, central data storage, a system like Sonos, smart home system, etc.
If it were my planning, I would buy a 24-port switch right away, so there would still be enough free slots for upgrades.
On the other hand, you can also start with a smaller switch and only upgrade or replace it if necessary.
It is difficult for me to give a concrete hardware recommendation, as it depends on your technical experience on one hand and, of course, how much money you want to spend.