I live wayyyyy up north in northern Wisconsin and keep my chicks in a refrigerator box (turned sideways, with no top - entails quite a bit of cutting and duct taping to re-design the box for use on one side!) in an unheated garage as early as April or May, when nights can get down to 30 or 40F.
I hang a heat lamp in the center of the box, and drape blankets over the two sides -- well away from the heat lamp -- and it stays quite toasty in there! I also put a few small holes in each side of the box to allow more air exchange. The high sides of the box eliminate drafts, keep the chicks in, and the blankets can be moved aside in the daytime when the garage heats up. I use clothespins to clip the blankets to the box, so they don't accidentally get moved towards the heat lamp or fall into the box.
If you MUST keep them indoors, what if you put them in a refrigerator box (which would prevent them from flying out) and then threw mosquito netting over the top, except for near the light? It might keep most of the dust and shavings in, but would still allow plenty of airflow. You could take the netting outside and shake it daily to get rid of accumulated dust.
You can cut a drop-down door in the side of the box so you can access the chicks whenever you want - and when you're not around, the "door" can be stuck back into its closed position and clipped with clothespins or tape.
I like a big fridge box, because if you hang a heat lamp in the center, or even to one side, it gives them plenty of room to move away from the light if it gets too warm.
I line my fridge box with an old shower curtain or plastic first, to keep the bottom from getting damp and falling apart. Then I put down a THICK layer of shavings - at least 4 inches. I use a kitty litter scoop to pick up poops that accumulate on top, and stir the shavings once daily to break up wet clumps and keep the bedding more fluffy and dry.
I have also used pine needles as bedding for broilers after 2 weeks of age, and it worked GREAT - better than shavings, as it didn't seem to absorb so much moisture and if raked/turned daily, stayed quite dry. And best of all, it was 100% FREE, so I didn't feel guilty changing it often! I put a thick layer of pine needles in my layers' outdoor run, too -- it gives them something to scratch around in and provides good drainage when it rains. A thick 8-inch layer packs down to around 3 inches after the hens romp around on it a few days, but it's still quite airy with spaces between the needles, and much nicer for me to walk on than "poo-muck." Seems easier to rake out the run when the poop is mixed into something.
As you can see, a big part of chicken ownership is poo management. You'll get used to it, and you'll find a system, and it won't seem so overwhelming.
Good luck!