Wood runs better up but which way is prevalent wind from? If it hits side with vent it will mess up wood and propane. Wood will create stains up the side of building if side vented.
If redoing wood.stove pipe please look at changing cheap light sheetmetal pipe with shedual 40 pipe same diameter. You will still.need the Insulated part through roof but you won’t have to worry about chine fires as the schedual 40 won’t burn from fire place heat.