What grit sandpaper to use after filling in nail holes to prepare wall

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Fine grit. 150 - 200 grit will work.
If youre using spackling you shouldn't need to sand. Make sure to remove excess with a plastic putty knife while wet, then wait until completely dry and clean with a large moist sponge.
If you're talking about joint compound, a fine grit is all that is needed, then follow up with a moist sponge.
What did you fill the holes with? If it was Spackle, I' d use a damp sponge.