You are in Connecticut so you do need a solid coop, or at least a place for them to get out of direct wind, especially when roosting. And for 30 chickens it needs to be fairly large since you'll get a lot of snow and they will be stuck inside it. Or find some way to keep an area clear of snow for them.
For $300 you'll have to scrounge for a lot of materials. On craigslist don't just look for sheds, look for lumber, roofing, hardware (hardware can get expensive), doors, windows, plywood, paneling, whatever you think you can use. You probably have a habitat re-use store around, check them out. Check out construction sites, they often use a lot of materials for construction aides or for forming concrete and have to dispose of it. A lot of stuff gets moved on pallets, then the pallets are excess. I'm not sure where you'd find them but a lot of people use pallets for raw material when building a coop.
$300 is a challenge, good luck!