If you want decent Wi-Fi throughout the whole house, you need to plan at least one Wi-Fi access point on each floor. Whether one is enough and where to place it needs to be considered based on the floor plan. Don’t forget coverage for the terrace and garden. Personally, I find access points on the ceiling the best and power them via POE. If you implement this consistently, you can put your router in the utility room and turn off the Wi-Fi there. For access points, I would choose Unifi.
For your network equipment, you need some space in the utility room. Either you nail the router, patch panel, and switch to the wall or use a Hager multimedia distributor. Personally, I always tend to go for a network cabinet.