By shopping list, am I correct in assuming that you mean things that Hester would purchase for herself and her daughter? If that is the case, then she would most definitely need to purchase red (scarlet) fabric. The scarlet fabric is so that she always has a supply with which to make the scarlet "A" on her dresses. In the novel, the Puritan community makes Hester to wear a scarlet "A" on her clothing at all times in order to mark her as a woman who committed adultery. Throughout the novel though, the reader discovers that Hester is a woman of remarkable talent, compassion, confidence, and inner strength, so much so that the town begins to forget that the "A" is meant for adultery and begins to associate the "A" with "able."
Hester would also need a needle and gold thread in order to sew on the scarlet "A." The novel says that Hester adorns the scarlet "A" with "fantastic flourishes of gold thread." She puts wonderful needlework into adorning her clothing with the scarlet "A."
I assume that her shopping list would also include clothing for her daughter Pearl, food, household items, and candles for night.