would use stove pipe inside and switch to SS pipe on the outside.
First off, you are going to get blasted for bypassing "code" on a woodburner in a garage or barn situation. Nobody has ever done that until now.

Now that is out of the road....do you have a ceiling in the area or is it an open area to the roof? If you have a ceiling, you will need to get a flue kit that has the stainless steel pipe, the transition box for the ceiling, and the proper flashing for the roof. If you are open clear to the roof, is it a metal roof? You will need stainless double wall pipe and the proper flashing. You can run heavy black single wall made for woodburners up to the double wall. DO NOT VENT THROUGH GALVANIZED pipe that is not made for woodburners. Any of the box stores can hook you up with the proper items you need, or if you have a woodburner store near you, best bet is to check it out for the proper hookup. Also when the flue is hooked up, make sure the female end of the pipe is up and the male end drops down into the top of it. By doing that, any creosote that would happen to buildup and run down, will run down into the preceding lower pipe and not run out through any gaps. Smoke will be drawn out through the pipe properly. A woodburner flue is opposite of the way a car exhaust is hooked up.