Alright, I can speak to this one big time as the wife granted me the rights to a game room in our house as well and I've been doing it for four years now, so I have some insight on things I wish I did better and things I did right.
First off, if it's a dark room you gotta go OLED, and a good game room should be pretty dark in my opinion. That being said, if you like an extremely bright display there are those who don't much care for OLED's in that sense, as they don't get quite as bright as high end LCD's, and keep in mind that different TV technologies will be on the rise in a few years, (mini LED being a very interesting one for bright rooms and a superior solution for that use case scenario), so there are a good few options right now and there's going to be more later, just something to remember.
Second, install some bias lighting behind your set before getting everything else installed man. I didn't do it, and I'm not going to now as it's just too much fuckin work to pull everything out now and get behind it all, but it would have made my set up far more relaxing on the eyes and just nicer looking in general, so don't skip that part bro, just spend the money, it's not that much in the long run.
Third, I promise your wife is not gonna like colossal HDMI cords going all through the house. She might say it's cool at first, but give it a year of her looking at it with disgust every time she walks by and I guarantee you she's gonna say it looks like shit at some point and that she wished there weren't cables along the walls/floors/ceilings, it's inevitable. For your use case scenario, the Steam Machine will be infinitely more utilitarian and generally pleasant to use and to organize and work with. That being said......
Fourth, so I have a downstairs entertainment center as well, and we have my Steam Deck OLED hooked up to that set up through dock. It honestly works fuckin great for tons of games and I love having it set up like that as I use it as an Emu Deck too, so it's basically a mobile retro station that I can also throw on the TV down there easily, which is a 1080p display, and the Steam Deck does great with most older games at 1080p so I'm pretty happy with it. That's the rub though, if you go with a nice modern OLED, it's gonna be 4k, which the Steam Deck's not anywhere near equipped to deal with, and the built in FSR isn't gonna help to that degree. That's why I have mine downstairs and not in the game room, as that's a 4k set and the Steam Deck honestly struggles with 1080 on tons of games, so I can't recommend that. If you've got a 1080 set somewhere, absolutely throw a Steam Deck on there, great fun, but I can't recommend it for your game room broseph, it just ain't got the grit you're gonna want in there.
I think that about covers it. Let me know if you've got anymore questions and I'll do my best, and congratulations on the house bro! It's a huge step and a lot of work, time, and money, but being a homeowner is honestly rewarding and fun, despite the almost constant stress of home improvement projects, repairs, remodels, expansions, wife's whims, all that shit. Still, wouldn't trade it, as I can't go back to apartment living, I need to be able to enjoy my entertainment center without annoying others
. Thanks for the tip man, so moonlight on the deck huh? I think I'll do that, thanks brethren!