What time of the year are you planning on getting them and what does your coop look like? How many chicks?
There are pros and cons to different approaches. To me, one big advantage to raising them in the coop where the older ones can see the is that it makes integration easier. Since you don't have any older ones that doesn't matter.
My brooder is in the coop. I've put chicks in it straight from the incubator when the outside temperature was below freezing. If your coop has good wind protection down low and good ventilation up high you can raise them out there in any weather. You may not even need a brooder out there, depending on what your coop looks like, since you don't have any others.
To me the big challenge to brooding outside is the temperature swings. I've had temperatures go from below freezing to in the 70's F within a 36 hour period. I've had temperatures go from in the 100's+ F to in the 70's day at night. What you need is to provide a place warm enough in the coolest temperatures and a place cool enough in the warmest temperatures. That will probably be pretty easy in that basement, could be more challenging outside.
I've found that chicks straight out of the incubator or straight from the post office are really good at regulating their heat requirements as long as they have the option. There are different ways to provide that warm spot. I use heat lamps but plenty of people brood them outside in all kinds of weather with heating plates, heating pads, or other methods.
They do generate a lot of dander and dust, a lot more than you would imagine. Part of that is bits of down and dead skin floating around. Part if it is due to their scratching. They create dust by scratching dry bedding and dried poop. That's a big reason to not brood them in the house. That looks like a water heater, maybe a furnace of some kind. Would dust bother that? Probably not but something to think of.
I also would not let them roam the full basement. Part of that is that when they are really young they might wander away from the heat and not be able to find their way back. After just a few days I would not worry about that, but it is possible they could get trapped behind something and not be able to get back. I've had adults get stuck behind a fence that desperately wanted to return to the coop at bedtime and ignored a gate just a few feet away that they had been using all day.
But the main reason is that they poop. Wherever they go they are pooping. And they like to perch on things. I'd expect within two weeks that they would be pooping on those stairs and possibly on the water heater and piping. If you confine them to a brooder you confine the mess.
Lots of people brood indoors and like it. But the dust, the noise, or (if you let the brooder get wet) the stink has some people that just can't wait to get those things out of their house. A lot of the difference is how you set it up. That basement looks like one of the better places I've seen for that.
Your options are wide open. Good luck!
