Choose the correct answer. I'm going to buy ____ books for the children.

The sentence requires a determiner that can be used with a plural countable noun ('books'). 'Much' is used with uncountable nouns. 'Some', 'lot of', and 'any' can be used with plural countable nouns. However, 'any' is typically used in negative sentences or questions. 'Some' and 'lot of' are suitable for affirmative statements. 'Lot of' implies a large quantity, while 'some' implies an unspecified quantity. Without further context, both 'some' and 'lot of' are grammatically plausible. However, 'lot of' is a more common and natural choice when expressing the intention to buy a quantity of books for children in an affirmative statement. Therefore, 'lot of' is the most appropriate answer.

I'm going to buy lot of books for the children.