There's ___ sugar at home.

The sentence is a statement, and 'sugar' is an uncountable noun. In affirmative statements with uncountable nouns, 'any' is typically used to indicate an unspecified amount or presence. Therefore, 'any' is the correct choice to fill the blank, forming the sentence 'There's any sugar at home.' This implies that if there is sugar, it's an unspecified quantity. The option 'no' would be used if the sentence were 'There's no sugar at home,' which is a negative statement. Since the sentence structure is affirmative, 'any' fits best in this context, although 'some' would also be grammatically correct and more common in affirmative statements. However, given the options, 'any' is the most appropriate choice for indicating the presence of an unspecified amount of sugar.