Fiberglass batts is usually the least expensive. Cellulose can be done on the flat part of the ceiling after a vapor barrier and drywall/paneling. Fiberglass will be a little easier for something quick.
You will need some of these to put on the roof side and extend a good 10" into the flat area. Then you can add a good R38 or more on the flat part of the ceiling. I can see daylight above your walls and presume you have some kind of ventilation. If not some roof vents will need added somewhere. Insulation will not work properly without ventilation.
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On the roof side if those are 6" rafters all you can fit is R19. For your walls, look to be 2X4 the most you can get is R13.
For your area vapor barrier is necessary regardless of type of insulation. Vapor barrier has to be on the heated side for NY.
UNLESS you do spray foam$$$