To plainly answer your question:
1) Keep your wireless router and disable the wireless network options, this will turn off the radio in it. You will want to use a decent router as it will have a decent firewall built in.
2) Get a decent quality gigabit switch because most likely you have more than 4 devices that will need an internet connection.
3) Go and buy a 1000 foot roll of CAT5e or CAT6 cable from your local hardware store, as well as a punchdown tool, Ethernet heads, and wall plates. Fish tape is also extremely handy.
4) Typically (though not always) the cable will come into your home underground before it goes in through a wall. If this is in a basement, then it become the prime place to set up all of your networking equipment. If it is a crawl space, then it sucks but you can get a coax extension to get it to reach a closet or other convenient location to store your router and switch. It helps keep things simple if this can be a central location in the home. In my own home there are limited options so I keep my cable modem over where the cable comes into my home, and then have an Ethernet cord that goes to a central place where all of my network equipment resides.
5) Get busy. Go look up some youtube videos about routing cables throughout your home, and get started doing a serious wiring project. Or hire someone to do it for you. This should be done properly in the walls away from electrical wiring, and avoiding any devices that put out a ton of electromagnetic interference (like fluorescent light bulbs). Keep each run under 300 feet.
Note that if you have an older home with plaster walls (like I do) then you may need to get creative. I ended up routing a lot of my cable through the HVAC duct work to avoid rebuilding half of the walls in my home. This is however not suggested as it is technically a fire hazard. Even though I did it, I am actively redoing my home little by little, and when I redo a room and have the walls open then I take the opportunity to put the wiring in correctly at that time... but one room every 2-3 years is going to take a while lol.
And that's it. Wired networks are typically DHCP, so there are no settings to change or anything; just plug and play.
Now, all of that said, I have a few thoughts about being afraid of Wifi as a health risk: It is moronic and stupid. Wifi typically runs on the 2.4GHz spectrum. There have been studies done on both 2.4 and 5GHz frequencies with no ill effects found. To shield yorself from all manmade 2.4GHz radiation then you need to turn off your flourescent and CFL lights, including the tubes found in the backlight of the monitor you are staring at right now. Also run away from pretty much any wireless devices including your phone, all cordless home phones, bluetooth devices like your console controllers, fitbit, headsets, wireless speakers, wireless headphones, just about any and all RC vehicles, or anything that sends information from point A to point B, because it pretty much all runs at or around 2.4GHz. It is a very crowded spectrum.
The reason why all of this 'electromagnetically sensitive' bull crap comes about is because there is another very powerful and very dangerous household item that uses that exact same frequency: The microwave oven. Consumer microwave ovens use 2.45GHz frequency (essentially 12cm light) to cook food, and will heat up just about anything in it's path with water in it. But there is a very good reason why a microwave oven is dangerous and why a wifi device is not. 2 in fact.
1) A microwave oven is using 650-1100 watts of power. Your wireless router uses a grand total of 10-20W (depending on age and quality), and much of that is running the internal parts rather than the antenna.
2) A microwave is using a very focused beam of energy to heat a surface area which is actually quite small. A wifi router is dispersing that much lower level of energy in (more or less) a sphere, which makes the radiation level ridiculously low when you are a foot away from it, and significantly lower when you are across a room or a house.
To put this in perspective, a decent FM radio station puts out 100,000 watts of power and we don't hear about DJs bursting into flame in the building right next to the tower for hours at a time day after day because that power is distributed over a spherical area. Put that into a beam, and it will kill you very quickly, and even standing a foot or two away from the tower is not exactly suggested. But it dissipates very quickly with distance, so it is not a problem to be some 20 feet from such a massively powerful EM source.
For that matter, you know what else puts out a whole bunch of 2.4GHz radiation? The f***ing sun puts out tons of 2.4GHz (and other much more potentially harmful) radiation which is just as capable of penetrating the walls in your home constantly for 8-16 hours a day in much greater quantities than a measly 20W wifi router which sends out bursts of transmission only when in use. How are you going to protect yourself from something as powerful as the sun? Good luck!
If you want something even remotely potentially harmful then look at cell phones from the 1990s. Those things put out a bunch of poorly regulated radiation out, and people put it next to their heads, and kept the things in their pockets. Yet, 20 years later we are not seeing reports about early cell phone adopters having any increase in brain or hip cancer, or any other form of potentially related ailments, even though at the time there were all sorts of news stories and 'studies' which talked about how all of that was going to happen. But my point is that if those powerful, leaky, inefficient, poorly regulated devices did not do any noticeable harm, then your much more efficient, lower powered, better regulated wifi router which is not sitting in your lap at all times is not going to do anyone any harm at all.
If you want to move off of Wifi for security reasons, or to have a more solid connection, or to cut down on cross-talk between your devices, that is all perfectly well and good, and there can be some legitimate concerns there (especially if you live in an apartment). But all of this talk about EM sensitivity is a bunch of superstitious crock that needs to be treated as the load of bunk that it is.
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