Use R-19 or R-21 kraft-faced fiberglass insulation for 2x6 walls to ensure it fits snugly without being too loose or too tightly packed.
The optimal choice for basement ceiling insulation is closed-cell spray foam. Key to basement insulation is controlling moisture, and closed-cell spray foam excels by providing a robust water vapor barrier.
For stapling insulation, 20-gauge staples are recommended, though 19-gauge and 23-gauge staples can also be used.