Kia Orana champ1410, welcome to the forum.
Food prices are more expensive in the Cook Islands, due to the isolation and logistics of importing foodstuffs onto our small nation with its low population. Also because there is not the same retail competition here as evidenced in NZ.
Passengers cannot bring in fresh fruits, and fresh vegetables in their personal luggage. But fresh meats and seafoods from NZ are allowed, along with groceries and you dont need an export permit from NZ for these items. If there are a number of people travelling in your same party you will likely find it more convenient to pack all your foods into a chilly bin with ice-bricks to retain keeping quality. Hopefully your island accommodation has a suitable fridge-freezer?
Itemise all your contents for Raro customs/ag inspection upon arrival. The major Saturday market is held at Punanga Nui which is situated close to Avatiu wharf (main harbour). There are small stalls dotted opposite CITC supermarket in Panama (near the harbour). More small owner-operated stalls in the outlying villages. Wigmore's Superstore sells what they grow. Most of the smaller village grocery stores stock a small range of fruit and veg too. You won't go short of supplies, including on Sundays.
Happy planning - kia manuia.