Re: rebuilding 1840s walls
I would recommend 1X4 furring strips 16" O.C. installed as Canuk indicated. It's a lot easier to hit with a screw or nail than a 1X3. That looks like roof sheeting above so remember you need to maintain air flow to prevent over heating the roof. If you use bat insulation, use unfaced but attach plastic sheeting to the rafters. And as stated above if you use closed cell foam no moisture barrier would be needed.
Be sure you live your life, because you are a long time dead.-Scottish Proverb