You should have two on hand, one for the wine, soft drinks, beer and water. The other for the chilled food. Place freezer packs in the bottom of the coolers before packing food. Packed in a cooler, they'll keep other foods cold in transit and will be thawed by picnic time. Always wrap foods like salad greens in double plastic bags and tape up screw-top bottles of dressing to avoid drippings.
Aluminum foil helps to keep warm foods warm and comes in handy for a quick clean-up of the grill.
Label every item in the hamper to avoid confusion over what is what on arrival. If you are grilling steaks, however, take a real knife and fork. I prefer real crystal glasses for my wine but plastic is preferred over styrofoam cups. Take along a corkscrew for wine and styrofoam holders for the frosty beers. Fruits and crunchy vegetables are always good and transport easily.