I've never done either...I've always just brought some items with me or shopped at a local supermarket/convenience store...Even if you're flying down and not renting a car it's possible...If you stay on site and take a bus from your resort to Pleasure Island there is a convenience store you can just walk to and load up on neccessities!
With the Dining Plan though, we haven't felt the need to buy additional snacks...In fact, we usually end up having snack credits left at the end of the trip that we use up and bring the food on the plane, train, in the car, etc. for the trip home!