In my house there are many floors with existing LAN cables, which provide internet. Now I would like to create a Wifi network from these, what do I need?
Routers usually have WAN input, correct? Do I need a repeater? Or a bridge?
You need WiFi access point for this task. Strangely, such devices are more expensive than those which provide multiple functions (Router/Bridge/etc). You can get any cheap WiFi router, connect to their LAN port (while not connecting WAN) and disable DHCP, then setup WiFi name and password. After that, if you will plug any LAN port of such device to your existing network, it will work as WiFi access point. You can have such as many as you need to cover the whole home. Use on all of these devices the same WiFi name (SSID) with the same password, but run them all on different radio channels. Optional but helpful, for easier managing such devices in a future, change LAN IP address on these WiFi access points to existing network schema. Make sure these IP addresses are out of current DHCP range set on your primary wired network.
Presumably you already have a router enabling the existing wired internet connection... in which case all you need are access points wired into the existing network.
If you don't have sufficient ethernet sockets in any given location to add an AP, then use [a] cheap ethernet switch[es] to add sockets. The structure ought to handle them without issue or require any manual configuration these days.
Let the existing router handle DHCP for the WiFI too.
Many domestic WiFi devices can be configured in one of 3 ways, bridged, DHCP & NAT or just DHCP. 'Bridged' makes it a simple access point & leaves your existing router in charge of IP Addresses & though-connectivity to the internet.