If the kids still needed diapers and wipes, I'd certainly send those ahead. Ditto if we were wedded to a particular beverage and needed to have a large supply on hand.
Since the kids are out of diapers and we are happy to rely on in-room coffee and free iced water for the week, we send ahead...nothing. We don't even check any luggage. We fit everything we need for a week (all clothes, shoes, meds, toiletries, autograph books, phone and camera chargers, breakfast cereal, snacks, disposable picnicware, etc.) into one 21" carryon for each person. Things the four of us might need on the plane (electronics, extra snacks, reading materials, sunglasses, wallet, etc.) go in our personal items (e.g., tote bag for me, backpack for DH). Sometimes, if luggage space is tight, I do bring an empty laundry bag and a sample-size container of detergent so we can pack fewer clothes and do a quick load of laundry on our mid-week afternoon at the pool, but those four small pieces of luggage and 2 personal items hold everything we bring -- and other than milk for our cereal, we've never needed to buy anything additional on site.