Personal Floatation Devices
Bulky or light, you're going to need one. I use the Force 6 Instructor Rescue Vest when not racing. It's a little on the heavy side but can pack a lot of extra snacks and other people's snacks. (Umm, oh... was that YOUR sports nutrition bar??)
It's a good idea to leash up for the kind of river where a swim could have unfortunate consequences. For that you'll need a quick release leash. The Force 6 vest comes with. It's also good for hanging onto those runaway kayaks once you herd them to the shore.
Most kayaking vests will work for riverboarding. Borrow a few if you can and decide what you like. Don't use an inflatable vest or something that will keep you minimally legal on a boat. Expect to pay upwards of $100 for a decent one.
Wondering what those black plastic squares with slits in them are used for? A river knife, of course! Great for slicing avocados or dipping into the peanut butter. Or for cutting yourself or a friend out of a bad situation. Just don't hit an artery, please. Might also come in handy for self defence, but probably isn't much use against a hunting bow.
A throw bag is another item that's very important to have if you're running anything serious, such as a waterfall or huge drop/hole. The bags here attach to your PFD.