To answer your question on how to train: do as many back-to-back training rides as you can over similar distances and terrain as you will encounter on the tour. When I trained for a similar tour in Tennessee in 2007 and 2008, I did a lot of Saturday and Sunday rides in the range of 65 miles or so, and I tried to ride some hills as often as I could.
As for packing: I'm not a light packer, especially if somebody else is carrying my bag. For the tours I've done, I bring enough jerseys and shorts so that I don't have to wear the same things twice. Arm and leg warmers, a rain jacket, and any other item you might want for cool mornings (ear warmer, long-fingered gloves) are handy. Of course, I'm not sure how cool your June mornings will be, but since most of those things take up little space, it's better to be safe than sorry. Beyond that, bring a handful of shorts and t-shirts that you can wear in the campground. Throw in a sweatshirt, some long pants, and a pair of sandals and you should be good. If you need to cut down on what you're bringing, try to focus on fabrics that you can get away with wearing multiple times--like wool.
For gear, I bring a spare tire, tubes, two water bottles, some extra snacks, my Road ID, an extra pair of gloves and sunglasses, and whatever else I might like to have "just in case," e.g., a spare cleat. I'm sure there are a handful of other things that I'm forgetting, but you get the idea. For the campground, I like to have a headlamp, earplugs, a camp chair, flip flops for showers, a quick-drying camp towel, and some stuff sacks so that I can keep my dirty/wet clothes separate from clean/dry.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher