Hi Elizabeth!
Welcome to the Walt Disney World Resort "No-Stroller Club"! As a mom who's been visiting the parks with my kiddos since they were tiny, I remember the days of strollers, diaper bags, and bringing everything but the kitchen sink with me to the parks. Now, as the mom of a recent high school graduate and an upcoming high school freshman, those days are precious memories! While the stroller was just as handy to carry around our "stuff" as it was to transport our kids around the theme parks, I don't miss trying to navigate through the crowds with it, or leaving it in Stroller Parking while we enjoyed rides and attractions.
These days, I still bring a backpack with me to the parks. My bag has all of the park essentials:
snacks, water, ponchos (for pop-up showers), and more. The good news is, for a normal-sized backpack, there's no need to find a place to store it during rides. As long as my bag isn't packed to maximum capacity, I usually have plenty of room to place it at my feet or in the storage pouch in the ride vehicle. The bag I carry is a regular-sized backpack, like a student would carry to school. I'm even able to carry my bag on thrill rides, such as Space Mountain and Rock 'n' Roller Coaster!
I hope this helps with your planning - have a magical day ! - Diane W.