I would also recommend Target over Publix for efficiency and cost. I shop at Publix weekly. In fact, I was there today. On a holiday weekend like today the store was so busy there were less than a dozen carts at the front and all the lanes, including self checkout, were backed up with lines. To have the groceries pre-purchased and delivered to the car will cost more than shopping in the store.
For Target, you place the order for pickup at least two hours prior to when you will arrive at the store. They will hold the order, so you could place the order before getting on a flight and they would hold it until you arrive. When they let you know the order is ready, you can either pick up inside store, or request delivery to your car curbside. There are no additional fees involved. If you are not a member of Target Circle, it’s free to join and you will get the best prices available. I don’t order from Target for pick up often, because Publix is across the street and Target is about five miles away, but I have picked up frozen pizzas a few times on a good sale, and they keep the order in a freezer until I get there, so I would have no concerns about buying perishables if you choose to.
It may come down to which one carries the items you want. My Target has a good sized grocery area, but it is still about half the size of my Publix store.