Definitely some sound deadening baffles along the walls/floor/top (which probably means using the larger, 48” culvert).
I’m not sure about filtration being needed on the outlet, but it probably would not hurt.
My basement is ‘non-air-tight’ enough that I could get good air flow by simply drawing air from the basement, down the culvert and out the vent at the end. I’d probably design a hatch or doors so I could close it off the culvert from the basement when not in use, and also leave the vent fan off unless the range was in use.