Any recommendation depends on your location - I wouldn't provide the same answer for Yuma, AZ as I might for Edmonton, AB.
When water vapor diffuses through a wall and reaches the exterior sheathing, if that sheathing temperature is below the dew point the vapor will condense. Depending on the amount of water vapor and the rate at which the wall cavity is able to dry out, this may lead to moisture problems.
Installing insulation in the wall cavity will help reduce heating costs, but won't address the problem of sheathing temperature. As a result, some builders are specifying 2" to 4" or more foil faced polyiso panels be installed outside of the sheathing to raise the temperature above the dew point. In these designs, some don't even advocate using cavity insulation. Vapor will still diffuse into the cavity, but it will not condense on the sheathing surface.
Installing foil faced polyiso on the interior of the wall, properly air sealed and with taped joints, forms an effective vapor barrier which will reduce the problem of moisture diffusing through the walls. However it may not solve all of the problems with vapor diffusion so it's quite possible to still have problems.
Additionally, while most people look to insulation as a primary solution for energy savings, often older homes would find greater benefit from air sealing. There is almost no way you can make an older house with plaster walls "too tight." In fact, the idea of houses being "too tight" is something of a myth. Your goal should be to have "managed ventilation" rather than the unmanaged ventilation common in older homes.
In my 1870's New England house as an "inside" solution I removed the plaster, installed fiberglass batt insulation in the cavities, applied 2" foil faced polyiso over the studs (for a thermal break and vapor barrier), with 1x3 furring strips and gypsum on top.
I grew up with vermiculite (now rare due to most of it being contaminated (in the ground) with asbestos), moved on to fiberglass, and am now a blown-cellulose convert.
They all work, for various values of "work."
Cellulose is inexpensive, gets MORE effective when cold, and blocks airflow well enough that a vapor barrier is (possibly) optional according to some researchers. It's dusty during install, but otherwise innocuous. I'd suggest getting a bale from each supplier (or each different brand from suppliers) and inspecting it - or from the supplier you'd go with on a cost basis (first) and if that fails your inspection, from others. I found the sample I got from a major home improvement chain was contaminated with a lot of scrap plastic; as it turns out, not only were the bales from my local home improvement non-chain cheaper per pound, they were also good clean cellulose with no plastic scraps.
Fiberglass compares well at 70F (where R values are measured) but gets quite terrible at -20F, just when you want it working hardest. It's far more prone to air movement (whether in batts, where seams are are a problem or as loose-fill.) Plus there's that whole scratchy thing going on with glass fibers.
According to "belt and suspenders" thinking and "it's cheap enough" my cellulose is sitting on top of a vapor barrier. One more way to stop air movement. Since your climate is primarily heating, your vapor barrier goes on the inside (generally, the "warm" side - complicated in climates where heating and cooling are similar.)
If you are not using the space beyond the wall, insulate the wall (and perhaps add some furring strips to get more insulation on the wall where there is room.) If you insulate the roof, you need to provide cold air channels against the roof surface to vent the roof appropriately (though with that steep of an edge, it might be difficult to get a serious ice dam, which is what roof venting/cold roof design is trying to prevent.)
Since you are gutting it, you may also want to furr out the endwall to make it thicker and give you more space for insulation, since you won't get a lot of R-value with any insulation in the space available. Alternately, and at higher cost, you could sandwich a layer of sheet-foam type insulation over the studs and under the drywall on that wall.
Generally you will also want at least a few cans of polyurethane spray foam. While you can do all your insulating with spray-foam, it's very expensive, relative to other kinds of insulation. But it's great for sealing irregular cracks and crevices.
Best Answer
The black is dust that is deposited by air leaks.
The best building framework is passive house and the perfect wall which orders your priorities. The first is liquid water, the seconds is air, the third is vapor and the last is insulation.
If you've gone to the trouble to open all the exterior walls to increase your insulation, I am going to assume that budget isn't the top priority.
I'd get aerobarrier to give you a quote for air sealing. https://aerobarrier.net
Once it was airsealed. I'd go with roxul for insulation. A passive house membrane like intello on the warm side of the insulation for moisture barrier. Then drywall like normal.
Big project, good luck !