This is related to the post where I wondered how we could best gather food for a temporary apartment, http://favoritefoodthisweek.blogspot.com/2014/12/eating-real-food-in-temporary-apartment.html , because this approach would also work for that. But it's also helpful for week-to-week or whatever grocery shopping.
I thought of it when my kids were in their late teens and said, ever so kindly (I really do have perfect kids, I'm serious) that they were not totally crazy about all the dinners I served. (Breakfasts and lunches, as I've done "forever," were always a matter of just keeping ingredients on hand for people to make themselves when they were ready.) I right away came up with this idea, and they were very happy with it: We'd all share meal planning and cooking, with me doing at most every other day's dinner; there was always the option to order in if The In-Charge-of-Dinner Person of the Day were too busy or tired (this was in New York where we had a gazillion inexpensive delicious options of real food to be delivered piping hot to our apartment door pretty much more quickly than I could cook it myself).
Actually, it's no surprise I thought of that, because even when they were quite little I'd say in say the cereal aisle, "We're low on cereal -- each of you choose your own favorite, though remember someone else might eat some of it," or similar in the cheese section....
One could use this team approach when shopping for that temporary apartment too, or any home when you were really low on groceries, as long as you indeed had at least most of your "eaters" with you. Here's a basic idea for such an approach -- it would probably best be divided up before you get to the grocery store:
Each person gathers their own favorite breakfast ingredients, though if you need a lot of, say, milk and coffee, assign them to one person so you don't end up with 4x more milk and coffee than you could ever use.
Assign someone to gather very general items for lunches, like cheese, beans, tuna, bread, fruit, salad, or just the right number of decent TV dinners.
Each person gathers the ingredients for [a fair fraction] of the dinners they will plan and make.
Assign someone else for your [other] basics, eg olive oil, balsamic, salt and pepper.
Assign someone to get non-food basics, such as paper towels, dish soap...
Set a time to meet near the check-out counter to check out on the same bill, with the understanding if someone says there that they need more time you'll re-meet at a later time -- or of course if there aren't a million people to coordinate, just call each other on your cell phones if they work in that store.