Every raft trip (full/partial/motor/non-motor) will have a specific packing list per the outfitter, and this will be provided once your trip has been decided on. Below is a video as well as a general rafting trip packing list which will give you a good idea of what you currently have and what you will need to purchase for your rafting adventure.
Partial Canyon trips which requires a hike up or down the bright angel trail, and a comfortable backpack is required as you will likely need to carry all of your clothing and hygiene products with you. Some itineraries qualify for the Duffel Service which allows for your things to be transported by Mule. In this case a duffel/gym bag is required.