Your trip is so soon. How exciting!
I usually carry a medium-sized backpack in the parks. You can read all about this in the answer to a very similar question
HERE. Disney Mom Laura provides her take on this topic
HERE. And Kara gives her opinion
HERE.
As to the "what do you do with your bag question," on most rides, you can just put your bag on the seat next to you and enjoy the ride. Some of the adventurous rides (Mission Space, Kali River Rapids) have special on-board pouches where you can secure your bag in your ride vehicle. On other rides, Big Thunder Mountain for example, I put my backpack on the floor of my ride vehicle with my feet through the straps. You can read more about this in the related questions
HERE and
HERE.
On a totally different topic, at least 10 of the Disney Moms Panelists will be at WDW on or around September 26. We're running -- or walking, or crawling :-) -- in the first ever Expedition Everest 5K race at the Animal Kingdom. Please stop and say "Hi" if you see any of us in the parks.