[Raven]

your exit hole i assume is thru the wall....yes?

so you have purchased a double walled metal sleeve
for the stove pipe to go thru i'd imagine to insulate the heat
from making contact with the wood ...

or is your plan to go straight up.... that doesn't
make the best use of the heat....but

your building though is fairly small so not really an issue.

above the stove you need some sheet rock or metal
and you need to have it inspected.