No, you do not need waterproof boots or a sleeping bag. A lightweight sleeping quilt will be lightweight and warm enough for the season, something rated for maybe 15 degrees Celsius or higher. I like sleeping quilts because they can be easily adjusted to accommodate you if you are sleeping warmer or cooler. Keep in mind that you can also wear additional clothing to bed if you a bit cool while sleeping. Here is an example:
http://www.campsaver.com/sea-to-summit-traveller-tr1-sleeping-bag-750-down
I do not care for waterproof backpacking or walking shoes. During the Vietnam war, we were issued boots with fabric uppers and leather lowers and the lowers had large holes in the sides for draining water. There was no expectation of keeping prolonged exposure to water out of the boots, so it was important not to trap water in the boot (or shoe, nowadays). Others swear BY waterproof footwear, many swear AT waterproof footwear. One thing is for certain, manufacturers have glomed onto "waterproof" as if there is a certainty to its implementation. Here is one take about the subject:
http://www.cleverhiker.com/blog/ditch-boots
Not a recommendation, but as a point of consideration in general: for the last several years of long-distance backpacking with 28 pound loads in the Cascade and Sierra Nevada and Rocky Mountains for thousands of miles on trail, I have used the New Balance Leadvilles. Now I am "auditioning" the Brooks Beast, and liking them pretty well. Even though you don't have a lot of time to pick-and-choose, there is still plenty of time for you to find something that will work for you.
If you go shopping for a shoe, take your backpack with about 20 pounds of weight and the sock that you will be using to walk in. When you try on shoes, put on the pack first prior to either measuring your foot or trying on the footwear. Then I would suggest that you strongly consider purchasing whatever size fits you in one size larger. There are other things to consider, but hopefully this may be of help.