I picked food, because I'd heard of people choosing that and getting a letter from mom with some fruit that wasn't native to their town. Sure enough, my island ended up having pears as its native fruit and I got a letter from mom a couple of days later with 3 peaches! I was super happy as I was hoping for either peaches or apples as my starting fruit, and although that didn't happen I pretty much started with one of those two fruits anyway
The sleeping bag one gives you a sleeping bag, the lamp one gives you a different lamp, the something to kill time one I think gives you a different radio. Not sure what the food answer gives though.
I chose sleeping bag and didn't get a sleeping bag. :<
But I also think the colors is just randomized. There aren't enough options for answers to account for the variations people have reported. People with my same fruit/airport color still have different color nook items.