Both....
Don't think I am being funny when I say this. Meaning keep your savings, and use your regular grocery money to stock up. Shop loss leaders, coupon, grow a garden, dehydrate, can and freeze this summer. Try to cut out more meat out of your diet, eat more whole grains buying them in bulk ( beans , rice, etc)When doing that stock your pantry , eat what you store, store what you eat and rotate. Once you start doing this you will have a full pantry and freezers , and you can do it off your grocery budget. I feed a family of 4 and others, mostly organic ( all organic grains, beans , rice) pasteurized grass fed beef and chicken etc on less then most families do it. But you have to be willing to shop in bulk, cook from scratch and bargain shop for things you will use. Don't stock anything whether free or not if you won't use it . It will waste your time, energy and space to store it. I am sure you probably do or know this just thought I would add for your thoughts. If you can add or concentrate on just a few things to buy each month before you know it , you will be stocked up. For instance this month for me was 50 pounds of oats, berries ( wheat grains to mill for my flours)
Look for the best prices, whether Sams, Costco, a co-op which I use, Azure Standard or bulk foods on line, or your regular grocery store. Know your prices. Buy only fruit and veggies in season. Cherry pick and know your sales ads and loss leaders.
Good luck to you.