ᐅ Internet Connection – Where Should the Router Be Installed? In the Utility Room?

Hello everyone,

I’m having trouble understanding my telecom connection. I’m a bit stuck, but it might not be that complicated.

Situation:
The telecom socket is in the utility room. I believe these are called TAE sockets. I also have one of these in the living room. There are LAN cable outlets in several rooms.

Where should the router be placed? In the utility room? Would that mean my telephone also needs to be moved to the utility room?
Or can I just use the TAE socket in the living room?
Or is it enough to just plug in the LAN cable and get online (just talking about the internet connection here)?

I know it’s probably not a big deal, but right now I’m confused.
I still need to get a router for Wi-Fi. Can I use any router I want? Telekom naturally wanted to sell me their latest one for about 120 EUR.

So many questions...