Many of the oldest writings found from Ancient Civilizations are of lists (like inventories and shopping lists). This was the best and most concise article I found on the subject, but I recently took a course on the subject using the textbook Classical Mythology by Mark Morford.

Cuneiform is one of the earliest systems of writing, 4th millennium BC, wedge-like markings usually on clay tablets. The form developed from pictographs (think Egyptians in the minimalist style). Already, one might argue, that writing was a sort of short hand to be used as a short-term memory aid. Long works typically weren't written down in the earliest times of writing as history and mythology was transferred orally. This changed as common symbol were better understood and the writing styles spread. One of the oldest tablets holding cuneiform is actually a list of items, most likely a inventory of items in the household.

However, you can imagine that using clay tablets as your source of shopping lists is a more difficult task to manage. The papyrus writing material in Ancient Egypt was more likely, and did, use writing for shopping lists and short notes.