Metal with 1" non combustible spacers between the metal and the wall/ceiling. And yes that will reduce the clearance required down to 12".You would need to check with your local code and rules, but I think a wood stove only needs like 3 feet of clearance above, as long as its properly ventilated. you can also install metal behind it and above it to protect what is behind the metal from heating up.
Top or cap must also be a minimum of 5' from combustible materials.Flue would need to be above roof line for stove to draw properly.
So, yes, I imagine it could be done as you suggested.
A stove in the basement has the concrete floor and block wall to satisfy the requirement for a non-combustible surround (assuming the basement is not finished). Routing the stove pipe straight up through the 1st floor, then ceiling, possibly 2nd floor, then another ceiling, and finally the roof can get messy and expensive unless you have a clear shot free of hidden pipes, ducts, and wiring. The pipe does not have to be straight all the way to the top to draw properly so my advice is to get it outside as soon as possible. I've seen installations properly and safely routed between the 1st floor joists exiting the house and taking a 90° up the side with a lot less cutting, sealing, and drama.
View attachment 257392
Go for it!