Re-mortaring the stone foundation on a Pennsylvania barn

Hi All - - - I bought a small farm property in Montgomery County, PA, with a 3 story barn included. The barn is in great shape and just needs a little cosmetic repair work to ensure a long life.
However, the first floor structure for the barn is stucco and stone, with the stucco starting to erode in several areas. I would like to start pointing the stone to ensure that the walls stay solid. (I'm okay doing this, as I worked for a plasterer for years, and I'm reasonably proficient with plaster work).
My question is this - - There are areas of stone where there is no mortar at all in place (up to 10-12 inches deep of loose stone).
I assume that I need to mortar as deep as I'm able, but I have some questions about the mortar mix (what mix to use), and also whether I should mortar in stages, or just blast in the full depth of the openings at one time and allow to cure.
I can add pictures if necessary, but would love to get some thoughts.

Oh - And I will not stucco over the stone - For the exposed areas, I'd like to backfill with mortar and then re-point to leave the stone revealed.

Always appreciate feedback from this site, so I'll look forward to your suggestions.

 

One of the concrete Pro's will be around...might be later or tomorrow.

In the mean time, I'd guess that if the place is as old as I imagine..they probably used lime mortar...which is not the same as the bagged stuff you buy now. Might want to Google that to get some info...