Awesome! I thought you meant a
new little prefab, not a used one, it might be bigger than I was thinking. In that case, make sure you clean and sanitize it really well with a bleach/water solution, then rinse and have it completely dried out before your chicks arrive. Chickens are notorious disease spreaders, and even if the "old" flock never showed signs of any sickness, they could have been carriers. Better to be safe. Chickens are pretty good at building immunities over time, but you don't want to bombard your little ones with some unknown possible illness.
So they should have most of their feathers by 4 wks old and could go straight to the coop. Probably won't need much supplemental heat (if any)... depending on outside temps. If you think it's too cold, you could always run an extension cord and try a
heating pad or similar... much safer than a heat lamp.
If you do end up building a new coop, keep this old one too, it'll probably come in handy... like a separation area for a sick or injured bird, or a brooder for new babies... probably! If you get rid of it, you'll end up wishing you still had it.