What type of insulation should I use in a knee wall?
As with any answer, you should check your local codes. However, Going with R-30 on top and R-13 on the sides is standard and will give you very good value. If you can, you should plan on putting R-30 into the 'diagonals' too, that is, where the rafters are above the knee-walls but below the ceilings. If you don't have enough room now, you can screw some 2x4s onto the bottom of the rafters to gain more room: it'll be worth it in the end. 

Two things to remember: you don't have to or want to insulate away from living space. So, from your diagram, you would insulate vertically up the knee walls, but don't insulate in the area you close off, as you won't gain any value from it. Two, make sure when you insulate the sloped area where the rafters are, make sure you put baffles underneath the plywood before you install the insulation, to leave space for air to flow from the soffit vents up to the ridge vent.