Some produce will last two weeks if it is refrigerated. Potatoes, apples, carrots, brussels sprouts, sometimes peppers and kiwi (if you buy it hard). Other things, like tomatoes, berries, grapes, green beans, pineapple, bananas, etc. won't make it two weeks. Milk depends on how far out the date is when you buy, and when you open it. Ultrapasteurized milk could conceivably last two weeks. Eggs will be fine, as will cheese, yogurt (depending on the date), and anything frozen.
We end up at Costco every week because we love their rotisserie chickens. Otherwise I think every other week would work great.