Internet, router, plan signal

Try wireless - if it's enough: OK.
Try with powerline adapters - if it's enough: OK
Wired is better.

I wouldn't approach it with theoretical fundamental questions but simply "play" with it. The equipment is not expensive.

At the staircase exit [see ] I would probably find an access point (or possibly just a repeater here) the most practical. Don’t you have an installation duct pretty much in the middle?
I don’t quite remember if you once marked in the floor plan where you live and where the cohouser does. For further current discussions on this topic see, among others:
The repeater/access point market is not really my thing – so I cannot reliably assess the relevance of whether the installation location (in NL, if I remember correctly) should be pointed out here.

I see it similarly: wireless "belongs" to nomadic users, cable laziness is rather a poor reason for it.

I rather think that wireless is state of the art.

Why should I go through the hassle of all those cables, just to be location-independent again? I want to work at home on my laptop or tablet, just as I do not want to commit to which wall my TV hangs due to the cable sockets. We stream 4K simultaneously on two TVs, at the same time a radio app is running and I’m sending data over Wi-Fi to my printer. And all of this without buffering. I don’t see any added value compared to a wired solution, except for the costs, time, and mess during the installation phase.

I would save myself the fuss with the cables and buy a current router (and not a five-year-old clunker from eBay) and set up repeaters in the house.

Oetti, it's not about stuffing the whole house with network sockets, but only for the places where it's best to put an access point. Repeaters are a good retrofit solution but for new buildings, in my opinion, a no-go. Above all, Wi-Fi across floors is usually very problematic.

I rather think that wireless is state of the art.

But only as far as "brainless" is modern Wireless cannot be "state of the art" (=English: "state of the art") because "wireless" is not a protocol. It only means "cordless" – nothing more and nothing less. Every – but really every – technology has advantages and disadvantages, so there is no "one system fits all." Every cable has its properties, and the same basically applies to "cordless cables" – because the latter are not virtual in the sense of existing only in the imagination but in the form of radio links. Every frequency has its associated radiation pattern – and that is not limited to the useful signal, which brings us immediately to the topics of "spillover loss" and "signal to noise ratio." WLAN & Wi-Fi are in this sense "unshielded" – with cables, that would be a clear indication to doubt HD compatibility. Therefore, I only use "cordless cables" for nomadic users. I watch a music clip on YouTube on the tablet, gladly on the terrace – sure, I don't want to trip over eighteen meters of cable there. But if I watch Rosamunde Pilcher with my beloved, then I want to have both hands free for cuddling; and against pressure marks on my thighs, I don’t put the flat screen with one meter diagonal on my lap but hang it on the wall opposite. It doesn’t hang down to the next flood there, you’re right about that, but of the eight possible hanging spots in the living room (or, at , only seven until the piano is removed), each is reasonably close to a network socket. Besides that, I expect around 2025 (at CeBit or "Jugend forscht," time will tell) a kind of "night vision goggles" with which you can make electrosmog visible. Whoever transmits everything that isn't "3" in the tree basically turns their cozy home into a furnished microwave. How seriously does one want that? Wireless is almost synonymous with Terabit requiring Gigahertz, which the average partygoer buying consumer electronics likes to ignore. By the way, the fact that there are such things as repeaters at all is not only related to "extending" radio links but also serves to repair dents experienced by the radiation "cone" or "sphere" through components etc. Incidentally, almost as many "experts" cannot explain the difference between repeaters and access points as there are cardinals who mispronounce the word "diocese." And one more thing to think about regarding "Wireless = State of the Art": a radio link can only replace a copper cable; state of the art would rather be fiber optic cables.

Oh dear... "State of the Art" and "Repeater" in one sentence or post. If you don't have cables for properly managed access points in the house, then at least a mesh system with a real, dedicated wireless backhaul. Especially when the load on the WLAN keeps increasing with all kinds of 4K streaming devices, a simple router with repeaters doesn't do anything at all. In my opinion, something like that still belongs wired today. You can check it out with tools like WiSpy.

If you want to rely exclusively on wireless, you have to deal with significantly more factors than just having a nice little Fritz repeater everywhere. Before doing something like that at home, you ideally simulate it and then adjust the system to reality on site. Unless you happen to have no neighbors within 50m all around, they sometimes still play a role.