For more info on these matters and prior questions and responses (many, many) on handling basement water issues, go to the Home >Basement Waterproofing link in Browse Projects at lower left.
The obvious first step is to try to get the water away from the wall entirely as much as possible - read the prior questions and suggestions for lots of ideas on where the water comes from and how to cut it off BEFORE it gets into your wall.
Slight moisture transmission through the wall by wicking and vapor diffusion from damp but not saturated outside soil can be handled, SOMETIMES, with a negative-side (indoor) sealer like hydraulic mortar, with a penetrating waterproofing agent like HydroStop, or for only vapor transmission, with an epoxy coating like HydroSeal. Unfortunately, most of them let enough moisture through that putting a normal studwall wall in front of it is iffy, even though an exposed wall might be okay. Also, short of injection treatments, none can be counted on to permanently stop actual free water flow.
This is true even with a vapor barrier installed behind the new wall because the moisture coming through the wall accumulates on the wall at the vapor barrier and molds and goes stagnant, even if it does not actually rot the new studwall. Remember, this is outdoors organic-tainted water we are talking, about not clear water, so it goes anaerobic and smells like a stagnant pond pretty quick - not what you want to find right after finishin the inside of your basement, though many, many thousands of people have that experience every year.
If you have any actual visible free water inflow, then short of very expensive grouting or chemical sealant injection into the cracks, stopping that type of water with a negative side barrier is pretty much a lost cause short of casting a reinforced concrete wall inside the existing one and structurally tied back to it, and with a rubble wall could actually cause structural instability, as it could raise the outside water level against the wall oer time, if you are getting enough seepage inside to drain the pressure from the interior of the wall. Even though it works, the problem is it becomes a case of chasing the leak, especially in stone walls, becauase when you seal one spot you just force the water to find another path through a little higher up or to the side, so it can become a case of additional injections every week or two for months on end. However, injecting the entire wall is prohibitively expensive for all but historic preservation or large government or commercial buildings because it is labor intensive and involves drilling holes in the wall every foot or two over the entire surface.
Therefore, your only viable solution that is likely to yield a satisfactory result is positive-side sealing and drainage - which means excavating entirely around the outside of the foundation walls wherever they have fill placed against them or are below ground level, and installing a waterproof barrier. This is tough with a stone foundation because of the roughness of the surface. While it is possible to parge coat (trowel overlay) the surface with portland cement to give a smooth surface to apply waterproofing to, that is all hand work and gets expensive to just provide a smooth surface. Likewise, a shotcrete or gunite sprayed cement surface smoothing coat is possible but too expensive for most residential projects.
All I would recommend, within reasonable cost, is (after any needed mortar repair) is a heavy sprayed asphaltic waterproofing coating directly on the stone to get full contact with the entire surface, with an overlying heavy duty (say about 20mil+ HDPE or modified PVC liner like Hypalon on it as the primary waterproofing barrier, attached at the footer with a waterproof asphaltic sealed batten strip and attached at the wall bottom plate at the top of the wall. Another possibility would be something like bituthene placed over a flexible plastic drainage mesh as a padding for it so it doesn't puncture when backfilled. Normally you would use a flexible waterproofing bitumastic like bituthene (asphaltic sheet) applied directly to the concrete or building block over a thin asphalt spray coat, but on a rubble stone wall that would undoubtedly puncture on the stones when backfilled. Then, to direct the majority of the water away from the waterproofing system, a french drain system and free-draining backfill, daylighted to open air with gravity drainage; or if that is not possible, then to a wetwell with sump pump to keep it dewatered around the foundation.
Because rubble and stone walls are of dubious strength (especially if 200 years old) and their stability is highly dependent on the skill of the builders, the stone resistance to weathering, and the shape of the stone pieces, I would really recommend you see a structural engineering firm with both a civil/geotechnical engineer familiar with foundation waterproofing and a structural engineer on staff (may be same person if cross-discipline educated and licensed), who can both, as necessary, contribute to the solution. A preliminary site visit and discussion about $250-350 probably, up to $1000 total including a test pit to inspect outside wallcondition and soil/water situation. Maybe $500-1000 more to design a fix and provide specs for a contractor to work to - and you should invest the $500-1000 or so additional for the engineer to be there during the first application of the selected fix and to inspect the job as it progresses.
Unfortunately, unless you are just talking moist surfaces with no free water infiltration which could be negative side sealed for $1500-3000 range typically, for an exterior sealing job you are typically looking at $7-25,000 range depending on house size and how much water there is coming into the excavation, and soil type. Another reason for an initial engineer's inspection - to help scope out your exact condition, and assess the alternatives that might work for you. Attention to the source of the water is critical here, because if you do not have a high water table situation, then roof runoff and surface drainage correction might totally eliiminate the need for positive side treatment, and allow you to go with interior surfacingonly, though I would still doubt you could safety put in interior walls without moisture issues.
I have a feeling you are not going to like the alternatives that are likely to be presented. I can see, based on my experience with several cases like this on 200 year old commercial and public buildings on the east coast, either a full exterior sprayed concrete surfacing plus sealant and drain for $15,000 plus, or localized injection from inside of silane or silica based sealants where the leaks are for maybe $3-5,000, and then leaving the interior surface exposed to allow continuous evaporation of water vapor getting through the wall, with basement dehumidification as necessary.
One VERY IMPORTANT NOTE - if you are talking a dry laid rubble stone foundation rather than a fully mortared wall, then stability during excavation beomces very important, and a deliberate inspection (with test pit to full depth) by a civil/structural engineer, for about $800-1000 probably (the same inspection and test pit I talked about before), should be done, and procedures established for how much wall can be excavated at one time without compromising stability. This is VERY critical - a lot of people have tried repairing dry stack rubble walls under old homes and ended up with partial structural collapses because the wall basically fell apart. Ditto is mortared but the mortar is badly degraded so it does not really hold all the stones in place, making it essentially stacked stone.
FYI - google this search term - This Old House rubble wall repair - and you will find several videos and articles and blogs on rubble wall repair and insulating and waterproofing, including one very good video at This Old House on the difficulties of working with rubble wall on a repair job.