Keep in mind that items must be packed quite snugly to avoid undue movement in transit. I've sent cookies to friends in Hong Kong, Tokyo and other faraway places. I made the cookies large, left plenty of moisture in them (so they wouldn't be hockey pucks when eaten) and I individually wrapped each one. When the mother of one of our overseas associates called to ask me how I got the cookies to her son overseas, I told her my method. She said, "The crumbs will taste just as good."
If you're doing cookies, make sure they're of a durable enough variety not to become crumbs when they arrive. Moisture + Fruit = Mush so wrap each of your fruits in gift tissue not plastic wrap. Once the basket is assembled and you're sure it's as secure as possible, wrap the entire thing in cling wrap. (There will be enough air to keep the fruit from rotting for a short time.) Then, place in a well-padded box and after folding the top, shake the box. If there is any movement, add more packing material. Overnight express is best for foodstuffs to ensure they're the freshest possible. Baskets are a great gift...unless they look like a science project/train wreck when received.
One thing to consider, gift wrap tissue paper is loaded with dioxin and PCPs which will leach into food with only short exposure. These are seriously toxic chemicals used in the production of non-food grade paper products. Try to find food-grade deli paper to use as tissue padding.
When shipping cookies or other breakable food items I wrap them in thin baking parchment or waxed paper, then wrap again in plastic and bubble wrap.