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 answer changes depending on location.
Because of a complete lack of actual fire incidents, four Western USA States: CA, OR, WA and ID petitioned for an exception to NEC 394.12 and permit insulating over Knob & Tube Wiring. In some places you must first file a Knob-and-Tube Wiring Safety Report, and everywhere else it's a good idea.
It is a complete myth that Knob & Tube must be air cooled. Instead measure the gauge of the wire and put in an appropriate AFCI breaker for the gauge, and you're done. 100 year old copper is just as good as modern copper, in regards to household use. You should remove from the K&T any high load devices. What's left, especially in the era of CFL's and LED's, won't draw enough current to cause a problem.
The insulation of the era was not all that good, and perhaps for that reason K&T does not depend on it. Ceramic tubes will outlast civilizations, and hold the wires apart even if the insulation is damaged.
You can even add an extra margin of safety by underrating the K&T (the opposite of depending on air cooling). For example if you find 12 gauge wire, put a 15 amp AFCI in place, and you're more than done. For 14 gauge wire, a 10 amp breaker might do nicely, even if they look at you funny at Home Depot. Home Depot probably won't have the right breaker, but you can brave DIY scorn at Grainger, or just order online.
See
You should, however, replace any fuses. Those are dangerous, even with Type S fuse bases.