Fins are what make the difference between riverboarding and floundering helplessly in a current. They give you force, direction and protection. You should choose fins that are comfortable, that give adequate thrust, and that allow you to make quick turns at the flick of an ankle. Invest in some decent fins made for bodyboarding. Unless it's the only thing available on your particular continent, do NOT use dive fins. The long blade makes them really hard to maneuver, and in the river your life can depend on being able to turn quickly.
Always use tethers, even if you have to pull the shoelaces out of your hiking boots as a substitute. The river will suck your fin off especially in a hole. I find that having a fin dangling from your ankle isn't as bad as losing it completely, but if the fin is also tethered from a velcro strap on the bootie, the chances of it coming off at all are minimized.
Probably every bodyboarder and perhaps riverboarder has used those bright blue and yellow Churchill fins. Good to average power. They're not likely to damage your feet. Buy
Fred Simpson himself gave me a pair to try out, but I got that ol' top of the foot pain. I have delicate feet. Too much pressure on the top of my foot and it's game over. You might be burly enough to use Vipers. Certainly they are one of the more powerful fins on the market. Buy
Lightest weight fin I've ever tried. Quick, maneuverable, powerful. Haven't tried them enough to know if they'll make my delicate feet ache.
Need help deciding which fin is right for you?
R.I.P. This Brazilian fin is a personal favorite. Unfortunately, they are no longer manufactured. After losing one in the ocean, I was forced to try other fins, keeping the remaining one so I was mis-matched. First I bought some Allys, which were painful on the first paddle-out I tried at a pounding rivermouth (bodyboarding). I bought some Pods and used one on my left foot all spring and summer. By the end of the summer a lump was forming on the top of my foot and the pain was becoming worse every time I went out. Granted, I was going out on the board almost 2x/week, sometimes more. I finally found a pair on a bodyboarding forum. I paid a lot for them but didn't care; these things last forever. My smaller size fins for warm water are over 12 years old and show no signs of wear.