We are usually based in a house or apartment when we visit Europe. Saturdays can be tricky because sometimes grocery stores are closed on Sundays, especially in smaller towns. I once had to plan a 1st birthday party for a one year old for our group of 9 when we arrived in a small town in Switzerland on a Saturday evening, don't want to have to do that again.
Here's how we get through the first day or two of setting up housekeeping in a new city. We usually bring ground coffee and a bag of muesli with us (space comes in handy for souvenirs later). We almost always bring a large bag of our favorite nut/fruit trailmix for snacking on the go. If you could get each of your party to take one favorite item in their suitcase that the whole family enjoys that would help stock the pantry.
When we arrive we check grocery store hours and get the rest of what we need for breakfast like milk, some lunch snacks like meat and cheese, and a quick dinner like roasted chicken, pasta, a bottle of wine and some local sauce. We also buy a few fresh fruits and vegetables but not too many as these are fun to pick up at the outdoor markets.
In Europe we always buy the non refrigerated boxed milks. Our son thought they were meant to be a personal size, kind of like putting a straw through the top like a juice box. You'll see, they are about the size of broth in a box here and are stored on the non refrigerated shelves. The trickiest thing is trying to figure out fat content in a different language.
We always take a nylon bag or two to the grocery store (look for comfortable handles) and empty out our backpack or my large Baggallini for the heavier things from the store.
For your host who has offered, keep it simple, you'll have some time to shop on your arrival day and everyone will want to go explore! Have fun.