you are not building a house, use 2" x 2" to frame the walls, use 3" by 2" to frame the roof/ceiling and remember where you put the timber joists, you will need to be able to find the timber framework when you want to hang heavy equipment so measure and mark where the joist timbers are for later the more you use in the roof/ceiling the better. i have never built a foam room but i have built lots of grow rooms from 2" x 2" sawn rough timber frame covered in 3/4" drywall. i use 2" because the drywall helps strengthen the 2" frame once it is screwed in place, and you can fill the gap with loft/attic insulation for heat and sound, you will have to build a sealed box over the window first and put a flange in for your 8" ducting to draw in fresh air, cut a hole in the inner room wall and draw the fresh air in. all your electrics/timers sockets etc will be between the inner and outer room space, you will make holes in the walls to run the cables through for power, i dont know what you can use as a door as i use a more solid material. if you vent an exhaust fan in to the rest of your house from the open window for the grow room without another window open your house will get warm and go in to severe positive pressure and this gives you a severe headache.
do not know what the fuck this other guy is on about saying pressure treated, after framing and building the room just seal the whole inner room with plastic and build a door.
if you want to see a room and door i did check my 2 posts here :
https://www.rollitup.org/grow-room-design-setup/432700-room-within-room-2.html