What type of chimney liner and vent pipe are required for a wood stove?

I am working to rehabilitate an old chimney for use by a wood stove. There will be approximately 18 ft from the wall chimney socket (this is probably not the correct name for it) to the chimney top on the roof. I plan to situate the stove right next to the socket, so not much exposed vent pipe from the stove to it should be needed.

Which kind of pipe should I use for the liner and for between the stove and the chimney socket? I did this very similar job before but for a radiator boiler and water heater, which both run on gas and for that I used Type B vent pipe that is twist and click. I imagine for wood stove I would need a different type of pipe.