Anything and everything you carry (or which others have suggested you carry) is of little or no use if you lack the knowledge of how to use them (and how not to), when to use them (and when not to). A throw bag, a knife, a rescue vest, a pin kit, ...., heck, even a whitewater boat itself! All can be the most important tool in the world or can be the most dangerous tool in the world. The difference lies in KNOWLEDGE and experience.
1) Take lessons. If not through a formal instruction program, then either through a local club, through well-experienced and helpful friends, or some other means. You are extremely unlikely to learn what you need to know, and to understand proper technique (what you are doing right and doing wrong) until it is too late if you just learn on your own.
2) Take a swift-water safety and rescue course. And not just once, but every couple years, to refresh your skills and learn new techniques. Every class (every instructor) is likely to have some slightly different perspective and some slightly different technique which may be valuable. It is not enough to just have a rope, a knife, a rescue vest . . . you have to know how to properly use them. And you have to PRACTICE these skills somewhat regularly, so you are confident when you need to use them!
3) Take a first-aid class, especially something specifically tailored to wilderness first aid and whitewater. Just as above, it is not enough to just carry a first-aid kit . . . you have to know how to use it.
4) Take a 'critical inventory' of yourself. Not just once, but ongoing. Every year you paddle, every day, every river, every rapids. Be aware of where your skills are. Be aware of how you are paddling, that day, that hour. Listen to your body! If you are having an 'off day', don't push it! If you are tired, don't push it! If your friends are egging you into doing something you are not comfortable with, ignore them and get different friends! (It is one thing to have friends encourage you to gently extend your limits, to challenge yourself just a touch outside your comfort zone. It's another matter entirely if they try to guilt you into doing something you are totally uncomfortable doing.)
5) Don't forget the two most important things. HAVE FUN! and DON'T DIE! These may seem obvious, but it's surprising how often they are overlooked. I have seen people who are so intent on pushing their limits (not just in class/difficulty, but also constantly pushiing/challenging themselves to bigger moves playboating) that it seems more like WORK than fun. I see people who will hardly bother boating if they can't 'go big', so they'll drive hours and hours to get that, rather than enjoy what may be closer at hand . . . they seem no longer to be able to enjoy smaller features and the sheer joy of being on moving water with other boaters.
Equipment lists are so dependent upon what type of boating you are doing. People inevitably build the list to extreme proportions, much of which are appropriate mostly for extreme boating -- wilderness rivers, overnight trips, and such. This is daunting (and over-kill) for someone just getting into the sport, who is likely to spend at least the near-term future on class II (and maybe class III) rivers, and likely places well-known (and frequented) by lots of boaters . . . places which are *generally* pretty free of the sort of hazards as will require pin kits, rescue vests, and other such specialized gear as those lists will include. I think the above list (while certainly incomplete) will serve you well regardless where your boating experience takes you.