I know you need to use a comma for a list of three or more items. Would I need to use commas in this sentence, or do the conjunctions replace the commas?
"I went to the store to buy apples and oranges and grapes."

The Comma is a misunderstood punctuation mark. It's primary function is to group ideas so that the intended meaning is crystal clear.

Your sentence has a conversational tone, where the use of 'and' instead of a comma after "apples" suits it better.

When we speak, our tone of voice and inflection adds to clarity, so the comma can be essential in written communication, such as in:

"For breakfast, you can select from eggs and bacon and bangers and mash and bubble and squeak."

In that sentence, the separate dishes are indicated by:

"For breakfast, you can select from eggs and bacon, bangers and mash, and bubble and squeak."