Hi there, Matthew! Thanks for bringing your question to planDisney!
Whenever I visit the Disneyland Resort, I have to come prepared with my water bottle, sunscreen, snacks, and a light jacket if I plan on staying in the parks after dark. And I bring all this along in a backpack, so I'm happy to tell you that bags are allowed at the Disneyland Resort. Just keep in mind that your bag must be smaller than 24" long x 15" wide x 18" high and cannot have wheels (like a suitcase). You will have to go through a security check to enter the parks and your bag will be subject to search.
When it comes to riding attractions, you'll be able to take your belongings with you when you ride. For the most part, you will simply put your bag at your feet in the ride vehicle. The only attraction that I don't suggest you do this on is
Grizzly River Run because you and your stuff will get soaked. Luckily, there are lockers located right by the attraction entrance that are free to use for the first two hours so you can store your bags while you ride. If you would rather not lug your stuff around all day, there are
lockers available to rent inside both parks and in the esplanade.
I hope this helps! Have a fabulous day!
-Linda